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arXiv · 1103.1097

Recovery of a source term or a speed with one measurement and applications

Plamen Stefanov·Gunther Uhlmann
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Abstract

We study the problem of recovery the source $a(t,x)F(x)$ in the wave equation in anisotropic medium with $a$ known so that $a(0,x)\not=0$ with a single measurement. We use Carleman estimates combined with geometric arguments and give sharp conditions for uniqueness. We also study the non-linear problem of recovery the sound speed in the equation $u_{tt} -c^2(x)Δu =0$ with one measurement. We give sharp conditions for stability, as well. An application to thermoacoustic tomography is also presented.

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Plamen Stefanov, Gunther Uhlmann. 2011-03-06. Recovery of a source term or a speed with one measurement and applications. https://arxiv.org/abs/1103.1097

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