Uniqueness and stability of an inverse kernel problem for type III thermoelasticity

In this paper, we establish a global Carleman estimate for a thermoelastic system of type III. Based on this estimate, we furthermore study an inverse problem of determining a spatially varying thermal kernel function. We derive Hölder stability for the coefficient inverse problem only by displacement measurements over a given subdomain ωω along a sufficiently large time interval and temperature measurements at time t0t0 over whole domain ΩΩ. The uniqueness for such an inverse problem is yielded as a direct result.