Determination of Source Terms in Diffusion and Wave Equations by Observations After Incidents: Uniqueness and Stability

Abstract

We consider a diffusion and a wave equations

$$∂^k_tu(x,t) =∆u(x,t)+\mu(t)f(x), x∈Ω, t>0, k=1,2$$

with the zero initial and boundary conditions, where $Ω ⊂\mathbb{R}^d$ is a bounded domain. We establish uniqueness and/or stability results for inverse problems of determining $\mu(t), 0