A property of exponential stability in nonlinear wave equations near the fundamental linear mode
type: Item
instance of: scholarly article
title: A property of exponential stability in nonlinear wave equations near the fundamental linear mode
zbMATH Open document ID: 0937.35010
DOI: 10.1016/S0167-2789(98)00169-9
published in: Physica D
publication date: 1999-12-06T00:00:00Z
review text: This paper considers the nonlinear second-order hyperbolic PDE \(u_{tt}-c^2u_{xx}=\varepsilon\psi(u)\), with the boundary conditions \(u(t,0)= u(t,\pi)=0\), where \(\psi\) is an analytic function such that \(\psi(0)=0\), \(\psi' (0)\neq 0\). A stability property, valid up to times exponentially large in \(1/ \varepsilon\), is proven for the neighboorhood of the trajectory of the linear mode with lowest frequency.
reviewed by: Francesco Calogero
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 37K45
zbMATH DE Number: 1374376
zbMATH Keywords: periodic solutions
zbMATH Keywords: Hamiltonian PDEs
author: Dario Bambusi
author: N. N. Nekhoroshev
MaRDI profile type: Publication
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full work available at URL: s0167-2789(98)00169-9
OpenAlex ID: W1976173011
description: scientific article; zbMATH DE number 1374376