Uniqueness of solution of an inverse source problem for ultrahyperbolic equations

TL;DR

This paper proves the uniqueness of solutions for an inverse source problem related to ultrahyperbolic equations by transforming it into a Cauchy problem and applying Carleman inequalities.

Contribution

It introduces a novel approach to establish uniqueness for inverse problems of ultrahyperbolic equations using Carleman inequalities.

Findings

Uniqueness of solutions is established for the inverse problem.

Reduction to a Cauchy problem facilitates the analysis.

Carleman inequalities are effectively applied to prove uniqueness.

Abstract

The aim of this article is to investigate the uniqueness of solution of an inverse problem for ultrahyperbolic equations. We first reduce the inverse problem to a Cauchy problem for an integro-differential equation and then by using a pointwise Carleman type inequality we prove the uniqueness.