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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

Shitao Liu 1, and  Roberto Triggiani 2,

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 coecients 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].
Keywords: Global uniqueness; Carleman estimate; Coupled hyperbolic equations.
Mathematics Subject Classification: Primary: 35R30, 35L10; Secondary: 49K20.
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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