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 tasks are correct. Using the Fourier method and integral equations, solutions to the problems are constructed in explicit form.

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