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Determination of an unknown source for a thermoelastic system with a memory effect

We study an inverse problem of determining a spatially varying source term in a thermoelastic medium with a memory effect. The coupling phenomena between elasticity and heat as well as the memory effect make such an inverse problem very complicated. We firstly prove a pointwise Carleman estimate for a general strongly coupled hyperbolic system, and then obtain a Carleman estimate for the hyperbolic thermoelastic system. Based on this estimate, we finally establish a Hölder stability for the inverse source problem only by making a displacement measurement on a given subdomain for sufficiently large times, provided the source be known near the boundary. The uniqueness for such an inverse problem is yielded as a direct result.