Uniqueness and stability for inverse source problem for fractional diffusion-wave equations

TL;DR

This paper addresses the inverse problem of identifying a spatial source in a fractional diffusion-wave equation using boundary measurements, establishing uniqueness and Lipschitz stability under certain conditions.

Contribution

It introduces a new unique continuation principle and proves Lipschitz stability for the inverse source problem with temporally independent coefficients.

Findings

Uniqueness of the inverse source under analyticity assumptions.

Lipschitz stability of the inverse problem.

Use of a new unique continuation principle.

Abstract

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the analyticity and the new established unique continuation principle provided that the coefficients are all temporally independent. We also derive a Lipschitz stability of our inverse source problem under a suitable topology whose norm is given via the adjoint system of the fractional diffusion-wave equation.