A novel method to solve inverse source problem for advection-diffusion equation from final data

TL;DR

This paper introduces a new approach to recover source terms in advection-diffusion equations using final temperature data, employing integral transforms and complex analysis to ensure uniqueness.

Contribution

The paper presents a novel method combining integral transforms and Liouville's theorem to solve the inverse source problem with guaranteed uniqueness.

Findings

Proves uniqueness of the inverse problem solution

Develops a method based on integral transforms and complex analysis

Provides theoretical foundation for source reconstruction

Abstract

In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is established by taking an integral transform and using Liouville's theorem (complex analysis).