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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • D. K. Durdiev

摘要

Abstract

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.