The limiting amplitude principle for the nonlinear Lamb system

T. V. Dudnikova

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 4 Miusskaya sq., Moscow 125047, Russia

Abstract: A system consisting of an infinite string coupled to a nonlinear oscillator is considered. For the system, the Cauchy problem with the periodic initial data is studied. The main goal is to prove the convergence of the solutions as $t\to\infty$ to time periodic solutions.

Keywords: the nonlinear Lamb system, the Cauchy problem, periodic initial data, the limiting amplitude principle.

UDC: 517.9

MSC: 35L10, 34D05, 35B40

Received: 27.06.2019
Revised: 13.10.2019
Accepted: 13.10.2019

Language: English

DOI: 10.15393/j3.art.2019.6571

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