Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference "Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

On inverse problem for system of hyperbolic equations with mixed derivative

The nonlocal boundary value problem for system of hyperbolic equations with parameter from two independent variables is considered on restangle. We investigate questions of the existence, uniqueness and finding classical solutions of the investigating inverse problem.
Nonlocal boundary value problems for systems of hyperbolic equations second order were considered by numerous authors. Sufficient conditions for the existence and uniqueness of a solution of such problems were obtained by various methods. The nonlocal boundary value problem with data on characteristics were considered in [1-2] by the method introduction of functional parameters. This method is a modification of the parametrization method [3] developed for the solution of two-point boundary value problems for ordinary differential equations. In the [4-5] the necessary and sufficient coefficient conditions for the well-posed unique solvability of nonlocal boundary value problem.
In the present communication the sufficient coefficients conditions of the unique classic solvability of the inverse problem - the nonlocal boundary value problem for system of hyperbolic type with unknown parameter are obtained and algorithm finding its solution are proposed.

[1] Asanova A.T., Dzhumabaev D.S. Unique Solvability of the Boundary Value Problem for Systems of Hyperbolic Equations with Data on the Characteristics, Computational Mathematics and Mathematical Physics, 42 (11) (2002), 1609-1621.
[2] Asanova A.T., Dzhumabaev D.S. Unique Solvability of the Nonlocal boundary Value
Problems for Systems of Hyperbolic Equations, Differential Equations, 39 (10) (2003),1343-1354.
[3] Dzhumabaev D.S. The signs unique solvability of linear boundary value problem for the ordinary differential equation, Computational Mathematics and Mathematical Physics, 29 (1) (1989), 50-66.
[4] Asanova A.T., Dzhumabaev D.S. Correct Solvability of a Nonlocal Boundary Value Problem for Systems of Hyperbolic Equations, Doklady Mathematics, 68 (1) (2003), 46-49.
[5] Asanova A.T., Dzhumabaev D.S. Well-Posed Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations, Differential Equations, 41 (3) (2005), 352-363.

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