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| Recovering of Damping Coefficients for a System of Coupled Wave Equations with Neumann Boundary Conditions: Uniqueness and Stability |
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Citation： |
Shitao LIU,Roberto TRIGGIANI.Recovering of Damping Coefficients for a System of Coupled Wave Equations with Neumann Boundary Conditions: Uniqueness and Stability[J].Chinese Annals of Mathematics B,2011,32(5):669~698 |
| Page view： 1893
Net amount： 1219 |
Authors： |
Shitao LIU; Roberto TRIGGIANI; |
Foundation： |
the National Science Foundation (No. DMS-0104305) and the Air Force Office of
Scientific Research under Grant FA 9550-09-1-0459. |
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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 = ΓnΓ1, 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. |
Keywords： |
Inverse problem, Coupled wave equations, Carleman estimate |
Classification： |
35R30, 35L10, 49K20 |
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