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RAGE theorem for power bounded operators and decay of local energy for moving obstacles. (English) Zbl 0705.35094

Summary: We prove a RAGE type theorem for power bounded operators. This problem enables us to obtain a local energy decay of the solutions of the wave equation in the exterior of a periodically moving non-trapping obstacle provided that the global energy is bounded. We study also the spectral properties of the monodromy operator in the case that the global energy is not bounded. For Dirichlet and Robin boundary problems for moving obstacles we establish the existence of the scattering operator assuming a local energy decay and a boundedness of the global energy. We treat simultaneously both cases of odd and even space dimension.

MSC:

35P25 Scattering theory for PDEs
35L05 Wave equation
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