Carleman estimates and an inverse heat source problem for the thermoelasticity system

Abstract

According to the linear theory of thermoelasticity, we consider a bounded and isotropic body Ω whose mechanical behaviour is described by the Lamé system coupled with the heat equation. Assuming null surface displacement on the whole boundary, we discuss the inverse problem of determining the heat source only by the observation of surface traction in a subdomain ω satisfying ∂ω ⊃ ∂Ω along a sufficiently large time interval. Our main result is a Hölder stability estimate for the inverse problem. For it, we prove a Carleman estimate for the thermoelasticity system. © 2011 IOP Publishing Ltd.