Global existence of solutions to a wave equation with damping and source terms
type: Item
instance of: scholarly article
title: Global existence of solutions to a wave equation with damping and source terms
zbMATH Open document ID: 1018.35053
published in: Differential and Integral Equations
publication date: 2003-03-13T00:00:00Z
review text: This paper deals with the following mixed problem: \[ \begin{cases} u''-\Delta u+g(u')= |u|^{q-1} u\quad & \text{in }\Omega \times\mathbb{R}_+,\\ u=0 \quad & \text{on } \Gamma\times\mathbb{R}_+,\\ u(x,0)=u_0(x),\;u'(x,0)=u_1(x)\quad & \text{in } \Omega,\end{cases} \tag{1} \] where \(\Omega\subset \mathbb{R}^n\) is a bounded domain with smooth boundary \(\Gamma=\partial \Omega\) and \(g\) is a real-valued function. The author proves global existence of solution for (1) and studies the asymptotic behaviour of solution to (1) when \(g\) does not necessarily have polynomial growth near zero.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 1832869
zbMATH Keywords: non-polynomial growth of the nonlinearity
author: Mohammed Aassila
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1832869