Lipschitz stability in an inverse problem for the wave equation

Details Lipschitz stability in an inverse problem for the wave equation Lipschitz stability in an inverse problem for the wave equation

2011-06-08

arxiv.org/abs/1106.1501v1

Mathematics

Analysis of PDEs

Scientific paper

We are interested in the inverse problem of the determination of the potential $p(x), x\in\Omega\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_\nu u$ on a suitable part $\Gamma_0$ of the boundary of $\Omega$, where $u$ is the solution of the wave equation $\partial_{tt}u(x,t)-\Delta u(x,t)+p(x)u(x,t)=0$ set in $\Omega\times(0,T)$ and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself.

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