### Chirkunov Y.A. Skolubovich Y.L.

## Submodels of generalized three dimentional porous medium model in the presence of non-stationary absorption or source

### Reporter: Chirkunov Y.A.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.The present report is devoted to the obtaining and investigating of the new nonlinear submodels of the fluid and gas motion in a porous medium using a generalized three-dimensional model of a porous medium in the presence of nonstationary absorption or a source. Analytic (mathematical) modeling is performed, which includes a group classification (using the algorithm proposed in [1, 2]) of the nonlinear differential equation of this model in order to identify the submodels that have nontrivial symmetries. For these submodels, formulas for the production of new solutions are obtained and invariant submodels are found. Some invariant solutions describing these invariant submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The obtained solutions can be used as tests in numerical calculations performed in the studies of filtration processes, in the study of the soils at the initial stage of construction of buildings and structures, in the development of oil and gas fields in the shales, and in other studies related to underground aero-hydrodynamics. These solutions will make it possible to assess the degree of adequacy of the obtained mathematical models to real physical processes, after carrying out experiments corresponding to these solutions, and estimating the resulting deviations.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

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