Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates

TL;DR

This paper studies inverse problems for a half-order time-fractional diffusion equation in any dimension, establishing Lipschitz stability estimates using Carleman estimates and the Bukhgeim-Klibanov method.

Contribution

It introduces a novel approach to inverse problems for fractional diffusion equations in arbitrary dimensions, providing stability estimates based on Carleman inequalities.

Findings

Lipschitz stability estimates for inverse problems

Application of Carleman estimates to fractional PDEs

Extension to arbitrary spatial dimensions

Abstract

We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some additional assumptions. We establish the stability estimate of Lipschitz type in the inverse problems and the proofs are based on the Bukhgeim-Klibanov method by using Carleman estimates.