American Institute of Mathematical Sciences

2011, 2011(Special): 1001-1014. doi: 10.3934/proc.2011.2011.1001

Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness

 1 Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States 2 Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904

Received  July 2010 Revised  April 2011 Published  October 2011

We study a uniqueness inverse problem 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 sub-portion $\Gamma_1$ of the boundary $\Gamma$, and over a computable time interval $T > 0$. Under sharp conditions on $\Gamma_0 = \Gamma\\Gamma_1, T >0$, we establish uniqueness of both the damping and potential coecients for each equation. The proof uses critically the Carleman estimate in [11], together with a suggestion in [8, Thm 8.2.2, p.231]. A Riemannian version would also hold, this time by using the corresponding Carleman estimates in [19].
Citation: Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001
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