Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

Abstract

Abstract For a parabolic equation in the spatial variable x=(x1,…,xn){x=(x_{1},\\ldots,x_{n})} and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component xn{x_{n}} by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.