Questions of Well-Posedness of Inverse Problems for Determining the Right-Hand Side of a One-Dimensional Parabolic Equation

In this paper, we study inverse problems of finding the right-hand side of a one-dimensional parabolic equation using additionally specified integral conditions regarding the solution of the first initial-boundary value problem for this equation. Sufficient conditions for the given functions are found, under which the stated problems are well-posed. Using the Fourier method and integral equations, solutions to the problems are constructed in explicit form.

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