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On scattering by obstacles. (English) Zbl 0757.35055

Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. II, 1145-1154 (1991).
[For the entire collection see Zbl 0741.00020.]
In this talk one presents a summary of different recent results in scattering theory related to the distribution of the scattering poles and the behaviour of the scattering phase. The Dirichlet problem for the wave equation in the exterior of several strictly convex disjoint obstacles is treated in more details. The link between the analytic prolongation of a function defined in terms of periodic rays and the existence of an infinite number of scattering poles with bounded imaginary parts is obtained. The so-called modified Lax-Phillips conjecture is proved for several small balls provided that some condition on their centers is satisfied.

MSC:

35P25 Scattering theory for PDEs
76Q05 Hydro- and aero-acoustics
78A45 Diffraction, scattering
35L05 Wave equation

Citations:

Zbl 0741.00020
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