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Leading singularity of the scattering kernel for moving obstacles. (English) Zbl 0729.35100
The authors consider the scattering kernel for a moving obstacle K; they assume K remains in a fixed ball for all \(t\in {\mathbb{R}}\), and the boundary \(\partial K\) moves with a speed less than 1. The leading singularity of the generalized scattering kernel is studied in the case of the Dirichlet and Neumann problems, for odd and even space dimensions, in the generic case and in the degenerate case, extending preceding results of J. Cooper and W. Strauss [J. Differ. Equations 52, 175-203 (1984; Zbl 0547.35075)]. The proofs use a new localization procedure and the calculus of pseudodifferential operators; other basic tools of the scattering theory are taken from the book of the first author [Scattering theory for hyperbolic operators (1989; Zbl 0687.35067)].
Reviewer: L.Rodino (Torino)

35P25 Scattering theory for PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators