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

Plamen Stefanov; Gunther Uhlmann

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

Analysis of PDEs 2011-03-08 v1

Authors: Plamen Stefanov , Gunther Uhlmann

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 $u_{tt} -c^2(x)\Delta u =0$ with one measurement. We give sharp conditions for stability, as well. An application to thermoacoustic tomography is also presented.

Keywords

wave equation source recovery speed recovery Carleman estimates uniqueness stability thermoacoustic tomography

Cite

@article{arxiv.1103.1097,
  title  = {Recovery of a source term or a speed with one measurement and applications},
  author = {Plamen Stefanov and Gunther Uhlmann},
  journal= {arXiv preprint arXiv:1103.1097},
  year   = {2011}
}

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