Article

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

D. K. DurdievBukhara State University, 200117, Bukhara, Uzbekistan

Russian Mathematicsjournal2026en

ABI

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.

Topics

Numerical methods in inverse problems Differential Equations and Boundary Problems Stability and Controllability of Differential Equations

Identifiers

DOI: 10.3103/s1066369x2670012x

Citations and references

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