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Inverse scattering at fixed energy for stratified media. (English) Zbl 1005.35092
Journées “Équations aux dérivées partielles”, Saint-Jean-de-Monts, 2 Juin au 6 Juin 1997. Exposés Nos. I-XVIII. Palaiseau: École Polytechnique, Centre de Mathématiques. Exp. No. 15, 7 p. (1997).
From the introduction: We describe work in progress on inverse scattering for the wave equation in a layered medium. We consider the wave equation in \(\mathbb{R}\times \mathbb{R}^n\), \(n\geq 3\), with a variable sound speed, \(c(x)\), \[ \partial^2_tu= c^2(x)\Delta u \] as a perturbation of the wave equation with a sound speed, \(c_0(x_n)\), which is a function of one variable, \[ \partial^2_tu=c^2_0(x_n)\Delta u. \] Under certain hypotheses we have the
Theorem. \(c_0(x_n)\) and the scattering amplitude at energy \(k^2\) determine \(c(x)\).
For the entire collection see [Zbl 0990.00048].

35R30 Inverse problems for PDEs
35L05 Wave equation
35P25 Scattering theory for PDEs
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