International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)
Frolenkov I.V. Romanenko G.V.On existence of Cauchy problems solutions for two-dimensional loaded parabolic equations and systems of special formReporter: Romanenko G.V.There are different methods using the overdetermination conditions to bring the inverse problem to the direct problem by the investigation of the coefficient inverse problems for parabolic equations (or systems) with the Cauchy data. One of them tells that the inverse problem is reduced to the non-classical direct problem for the loaded (containing traces of unknown functions and their derivatives) equation (or system of loaded equations). You have to know the conditions under which these auxiliary problems are solvable, as well as to know the properties of their solutions. The sufficient conditions of the existence of solutions in classes of smooth bounded functions were found in the paper:
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