Unique determination of a time-dependent potential for wave equations from partial data

Abstract

We consider the inverse problem of determining a time-dependent potential $q$, appearing in the wave equation ${\partial }_t^{2}u-\Delta u+q(t,x)u=0$ in $Q=(0,T)\times \Omega$ with $\Omega$ a $C^2$ bounded domain of ${\mathbb{R}}^n$, $n\ge 2$, from partial observations of the solutions on $\partial Q$. We prove global unique determination of a coefficient $q\in L^{\infty }(Q)$ from these observations.

arXiv commentThe previous version of the paper arXiv:1406.5734 is now decomposed into two different papers with a new uniqueness result (that improves the previous one with weaker conditions and extension to the case of dimension 2) stated in the present paper and a new stability estimate (with different approach than the pervious version and extension to the case of dimension 2) stated in arXiv:1406.5734

References in corpus (1)

• A new approach to hyperbolic inverse problems

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