The inverse problem for the heat equation with reflection of the argument and with a complex coefficient
Elmira MussirepovaScientific Center for Theoretical and Applied Mathematics and Department of Mathematics, M. Auezov South Kazakhstan University, Tauke Khan, 5, 160012, Shymkent, KazakhstanAbdissalam SarsenbiScientific Center for Theoretical and Applied Mathematics and Department of Mathematics, M. Auezov South Kazakhstan University, Tauke Khan, 5, 160012, Shymkent, KazakhstanAbdizhahan SarsenbiScientific Center for Theoretical and Applied Mathematics and Department of Mathematics, M. Auezov South Kazakhstan University, Tauke Khan, 5, 160012, Shymkent, Kazakhstan
2022en
ABI
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Abstract The paper is devoted to finding a solution and restoring the right-hand side of the heat equation with reflection of the argument in the second derivative, with a complex-valued variable coefficient. We prove a theorem on the Riesz basis property for eigenfunctions of the second-order differential operator with involution in the second derivative. We establish the existence and uniqueness of the solution of the studied problems by the method of separation of variables
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