On the transient acoustic scattering by a flat object. (English) Zbl 0719.35063

This paper deals with the transient acoustic scattering in the particular geometry of a flat object (crack) in \(R^ 3\). The boundary integral for the crack opening displacement is studied as a spatial pseudo- differential equation with the frequency variable as a parameter varying in the half-plane \(\{\) im \(w\geq 0\}\). Existence, uniqueness and continuous dependence of the solution with respect to the data are obtained in the framework of Sobolev spaces of causal functions.
Reviewer: Tuong Ha-Duong


35P25 Scattering theory for PDEs
35L05 Wave equation
35S15 Boundary value problems for PDEs with pseudodifferential operators
76Q05 Hydro- and aero-acoustics
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