Geodesic
Inverse coefficient problem for a wave equation in a bounded domain
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 1, pp. 115-126

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The nonlinear inverse problem for a wave equation is investigated in a three-dimensional bounded domain subject to the Dirichlet boundary condition. Given a family of solutions to the equation defined on a closed surface within the original domain, it is required to reconstruct the coefficient determining the velocity of sound in the medium. The solutions used for this purpose correspond to the acoustic medium perturbations localized in the neighborhood of a certain closed surface. The inverse problem is reduced to a linear integral equation of the first kind, and the uniqueness of the solution to this equation is established. Numerical results are presented. 
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     title = {Inverse coefficient problem for a~wave equation in a~bounded domain},
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     number = {1},
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M. Yu. Kokurin; S. K. Paǐmerov. Inverse coefficient problem for a wave equation in a bounded domain. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 1, pp. 115-126. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_1_a7/