On finite fractal dimension of the global attractor for the wave equation with nonlinear damping
type: Item
instance of: scholarly article
title: On finite fractal dimension of the global attractor for the wave equation with nonlinear damping
zbMATH Open document ID: 1030.35017
DOI: 10.1023/A:1020756426088
author: Dalibor Pražák
published in: Journal of Dynamics and Differential Equations
publication date: 2003-03-11T00:00:00Z
review text: The author considers the following nonlinear wave equation \[ u_{tt}+g(u_t)-\Delta u + f(u) =0, \quad x\in \Omega,\;t>0, \] \[ u(x,t)=0, \quad x\in \partial \Omega,\;t>0, \] \[ u(x,0)=u_0(x),\;u_t(x,0)=u_1(x), \quad x\in \Omega. \] If \(f\) and \(g\) are smooth and satisfy some polynomial growth conditions, then the global attractor associated with this equation has a finite fractal dimension.
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 1879631
zbMATH Keywords: polynomial growth conditions
zbMATH Keywords: nonlinear wave equation
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
full work available at URL: a:1020756426088
OpenAlex ID: W98888228
description: scientific article; zbMATH DE number 1879631