On a class of inverse problems for a heat equation with involution perturbation

TL;DR

This paper investigates inverse problems for a heat equation with involution perturbation under various boundary conditions, establishing existence, uniqueness, and solution convergence using series expansions.

Contribution

It introduces new theorems on existence and uniqueness for these inverse problems with different boundary conditions, and provides explicit series solutions.

Findings

Proved theorems on existence and uniqueness.

Derived solutions via series expansion.

Discussed convergence of solutions.

Abstract

A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence and uniqueness of solutions to these problems are presented. Solutions are obtained in the form of series expansion using a set of appropriate orthogonal basis for each problem. Convergence of the obtained solutions is also discussed.