Inverse Problem of Determination of Absorbtion Coefficient in Parabolic Equation in a Plane

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Abstract


We consider existence and uniqueness of solution for the inverse problem of determination of the unknown coefficient α(x) at the u(t,x) in nondivergent parabolic equation in a plane. The additional information is given by @op@prepare∫ 0Tu(t,x)χ(t)dt, with χ(t) being the weight function. It should be noted that the coefficients of the equation depend both on time as well as spatial variable. For the problem concerned we obtain conditions sufficient for the existence and the uniqueness of generalized solution. We adduce the examples of the inverse problems satisfying the conditions imposed.

V L Kamynin

National Research Nuclear University MEPhI

Кафедра высшей математики; Национальный исследовательский ядерный университет «МИФИ»; National Research Nuclear University MEPhI

T I Bukharova

National Research Nuclear University MEPhI

Email: bukharova_t@mail.ru
Кафедра высшей математики; Национальный исследовательский ядерный университет «МИФИ»; National Research Nuclear University MEPhI

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Copyright (c) 2011 Камынин В.Л., Бухарова Т.И.

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