Determining the potential in a wave equation without a geometric condition. Extension to the heat equation

Ammari, Kaïs; Choulli, Mourad; Triki, Faouzi

doi:10.1090/proc/13069

Determining the potential in a wave equation without a geometric condition. Extension to the heat equation
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by Kaïs Ammari, Mourad Choulli and Faouzi Triki PDF

Proc. Amer. Math. Soc. 144 (2016), 4381-4392 Request permission

Abstract:

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work is that no geometric condition is imposed to the sub-boundary where the measurements are made. Our results improve those obtained by the first and second authors in an earlier work. We also show how the analysis for the wave equation can be adapted to an inverse coefficient problem for the heat equation.

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