Heat Source Determining Inverse Problem for non-local in time equation

TL;DR

This paper addresses the inverse problem of identifying a time-dependent heat source in a non-local in time equation within a Hilbert space framework, establishing well-posedness through operator reduction.

Contribution

It introduces a novel approach to prove well-posedness of the inverse heat source problem in a general Hilbert space setting, extending existing methods.

Findings

Proved the inverse problem is well-posed under general conditions.

Reduced the inverse problem to an operator equation for the source.

Established a framework applicable to non-local in time equations.

Abstract

In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing the problem to an operator equation for the source function.