Inverse problem for a subdiffusion equation with the Caputo derivative

TL;DR

This paper addresses the inverse problem of identifying the source term in a subdiffusion equation with Caputo derivative on an N-dimensional torus, proving existence, uniqueness, and reconstruction methods.

Contribution

It introduces a Fourier-based approach for solving the inverse problem in a general elliptic setting with fractional derivatives, establishing conditions for solution uniqueness.

Findings

Proved existence and uniqueness of solutions for the inverse problem.

Developed a Fourier method for reconstructing the unknown source.

Established conditions for initial data and additional constraints.

Abstract

The article investigates an inverse problem of determining the right-hand side of a subdiffusion equation with Caputo fractional derivative whose elliptic part has the most general form and is defined on an N-dimensional torus T N . The Fourier method is used to prove theorems on the existence and uniqueness of the classical solution of the initial-boundary value problem and on the unique reconstruction of the unknown right-hand side of the equation. Requirements for the initial function and for the additional condition are established under which the classical Fourier method can be applied to the inverse problem under consideration.