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 $\bar{M}$.

18 pages. arXiv admin note: substantial text overlap with arXiv:2211.06650