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

2011/03/06 by Stefanov, Plamen, Uhlmann, Gunther · 2 citations
#35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1103.1097

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 -c²(x)Δu =0 with one measurement. We give sharp conditions for stability, as well. An application to thermoacoustic tomography is also presented.

Cited by

• Recovery of Sturm-Liouville operators from partial boundary spectral data and applications
• Uniqueness and stability in determining the wave equation from a single passive boundary measurement

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