Recovering of Damping Coefficients for a System of Coupled Wave Equations with Neumann Boundary Conditions: Uniqueness and Stability |
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Authors: | Shitao LIU and Roberto TRIGGIANI |
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Institution: | [1]Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA. [2]Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA; Department of Math-ematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia |
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Abstract: | The authors study the inverse problem of recovering damping coefficients for two coupled hyperbolic PDEs with Neumann boundary
conditions by means of an additional measurement of Dirichlet boundary traces of the two solutions on a suitable, explicit
subportion Γ1 of the boundary Γ, and over a computable time interval T > 0. Under sharp conditions on Γ0 = Γ\Γ1, T > 0, the uniqueness and stability of the damping coefficients are established. The proof uses critically the Carleman estimate
due to Lasiecka et al. in 2000, together with a convenient tactical route “post-Carleman estimates” suggested by Isakov in
2006. |
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Keywords: | Inverse problem Coupled wave equations Carleman estimate |
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