Asymptotic completeness of scattering in the nonlinear Lamb system for nonzero mass期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Asymptotic completeness of scattering in the nonlinear Lamb system for nonzero mass

Authors:	A.?I.?Komech author-information" > author-information__contact u-icon-before" > mailto:alexander.komech@univie.ac.at" title=" alexander.komech@univie.ac.at" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,A.?E.?Merzon

Affiliation:	1.Faculty of Mathematics of Vienna University,Wien,Austria;2.The Institute for the Information Transmission Problems of RAS (Moscow),Moscow,Russia;3.Institute of Physics and Mathematics,University of Michoacán of San Nicolas de Hidalgo,Morelia,México

Abstract:	We establish the asymptotic completeness in the nonlinear Lamb system with nonzero mass for hyperbolic stationary states. For the proof, we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point, using the Banach space Inverse Function Theorem and a priori estimates. We give a counterexample showing that the hyperbolicity condition is essential.

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