Determining coefficients of thermoelastic system from boundary information

Abstract

Given a compact Riemannian manifold $(M,g)$ with smooth boundary $\partial M$, we give an explicit expression for full symbol of the thermoelastic Dirichlet-to-Neumann map $\Lambda_g$ with variable coefficients $\lambda,\mu,\alpha,\beta \in C^{\infty}(\bar{M})$. We prove that $\Lambda_g$ uniquely determines partial derivatives of all orders of the coefficients on the boundary. Moreover, for a nonempty open subset $\Gamma\subset\partial M$, suppose that the manifold and the coefficients are real analytic up to $\Gamma$, we show that $\Lambda_g$ uniquely determines the coefficients on the whole manifold $\bar{M}$.