Inverse Problem of the Thermoelastic Plate System with a Curved Middle Surface and Memory Term

This paper is concerned with an inverse problem of a coupled thermoelastic plate model. Two major features are that the thermal equation has a memory effect, while the plate equation has a curved middle surface. A differential geometric approach is developed, by which we study the pointwise Carleman estimates for elliptic and hyperbolic equations. We are able to prove a key Carleman estimate for the strongly coupled system. From them, the Hölder stability in recovering the source terms and the coupling coefficient is obtained. The measurements of the plate deflection and temperature are assumed to be taken on a subdomain of the boundary.