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Determining the Coefficients of the Thermoelastic System from Boundary Information

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  • Xiaoming Tan

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

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 Λ g with variable coefficients λ , μ , α , β ∈ C ∞ ( M ¯ ) . We prove that Λ g 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 Λ g uniquely determines these coefficients on the whole manifold M ¯ .

Suggested Citation

  • Xiaoming Tan, 2023. "Determining the Coefficients of the Thermoelastic System from Boundary Information," Mathematics, MDPI, vol. 11(9), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2147-:d:1138814
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