Inverse problems for q-analogue of the heat equation

TL;DR

This paper investigates inverse problems related to a q-analogue of the heat equation, focusing on weak solutions, spectral methods, and integral and final time conditions for source and initial problems.

Contribution

It introduces spectral expansion techniques to solve inverse source and initial problems for the q-analogue of the heat equation, expanding the theoretical framework.

Findings

Derived series solutions using spectral expansions.

Established conditions for inverse source and initial problems.

Provided analytical methods for q-analogue heat equations.

Abstract

In this paper we explore the weak solution of a time-dependent inverse source problem and inverse initial problem for $q$-analogue of the heat equation. As an over-determination condition we have used integral type condition on space-variable (in the case of inverse source problem) and final time condition (in the case of inverse initial problem). Series form of considered problems have been obtained via the method of spectral expansions.