Determining the Coefficients of the Thermoelastic System from Boundary Information

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

Mathematics, 2023, vol. 11, issue 9, 1-22

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 ¯ .

Keywords: thermoelastic system; thermoelastic Calderón’s problem; thermoelastic Dirichlet-to-Neumann map; inverse problems; pseudodifferential operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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