Carleman estimate for a strongly damped wave equation and applications to an inverse problem | Zendy

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Carleman estimate for a strongly damped wave equation and applications to an inverse problem

Author(s) -

Wu Bin

Publication year - 2012

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1570

Subject(s) - mathematics , inverse problem , wave equation , uniqueness , mathematical analysis , hyperbolic partial differential equation , inverse , damped wave , boundary value problem , inverse hyperbolic function , boundary (topology) , kernel (algebra) , partial differential equation , geometry , pure mathematics

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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