Qualitative analysis of a nonlinear wave equation
type: Item
instance of: scholarly article
title: Qualitative analysis of a nonlinear wave equation
zbMATH Open document ID: 1047.35103
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-06-18T00:00:00Z
review text: The author studies the boundary-initial value problem to the equation \[ u_{tt}-a\triangle u+bu_t| u_t| ^{p}=cu| u| ^{q},\quad x\in \Omega \subset \mathbb R^n,\;t>0, \] where \(a,b,c,p,q\) are positive constants, \(p\geq q.\) He proves that a solution of the problem in an unstable set is global but not uniformly bounded and characterizes all bounded global solutions. Moreover, necessary and sufficient conditions for convergence of bounded solutions as \(t\rightarrow \infty \) are given.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 2075944
zbMATH Keywords: nonlinear dissipation
zbMATH Keywords: source term
zbMATH Keywords: blow-up
zbMATH Keywords: global solution
zbMATH Keywords: convergence to equilibria
zbMATH Keywords: decay rate
author: Jorge Alfredo Esquivel-Avila
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: dcds.2004.10.787
OpenAlex ID: W2000914750
DOI: 10.3934/DCDS.2004.10.787
description: scientific article; zbMATH DE number 2075944