Determining the Coefficients of the Thermoelastic System from Boundary Information

Abstract

Given a compact Riemannian manifold (M,g) with smooth boundary ∂M, we give an explicit expression for the full symbol of the thermoelastic Dirichlet-to-Neumann map Λg with variable coefficients λ,μ,α,β∈C∞(M¯). We prove that Λg uniquely determines partial derivatives of all orders of these coefficients on the boundary ∂M. Moreover, for a nonempty smooth open subset Γ⊂∂M, suppose that the manifold and these coefficients are real analytic up to Γ. We show that Λg uniquely determines these coefficients on the whole manifold M¯.