Determining coefficients of thermoelastic system from boundary information

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