Carleman estimate for a strongly damped wave equation and applications to an inverse problem |
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Authors: | Bin Wu |
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Affiliation: | College of Mathematics and Physics, Nanjing University of Information Science and Technology, , Nanjing, 210044 China |
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Abstract: | In this paper, we establish a Carleman estimate for a strongly damped wave equation in order to solve a coefficient inverse problems of retrieving a stationary potential from a single time‐dependent Neumann boundary measurement on a suitable part of the boundary. This coefficient inverse problem is for a strongly damped wave equation. We prove the uniqueness and the local stability results for this inverse problem. The proof of the results relies on Carleman estimate and a certain energy estimates for hyperbolic equation with strongly damped term. Moreover, this method could be used for a similar inverse problem for an integro‐differential equation with hyperbolic memory kernel. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | Carleman estimate strongly damped wave coefficient inverse problem uniqueness stability |
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