Blowup of solutions of a nonlinear wave equation
type: Item
instance of: scholarly article
title: Blowup of solutions of a nonlinear wave equation
zbMATH Open document ID: 1001.35086
DOI: 10.1155/S1110757X02000281
author: Abbes Benaissa
author: Salim A. Messaoudi
published in: Journal of Applied Mathematics
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49597
review text: Summary: We establish a blowup result to the initial-boundary value problem \[ \begin{matrix} {\l}\qquad & {\l}\\ u_{tt}-Au+ku_t=|u|^{p-2}u, & x\in\Omega,\;t>0,\\ u(x,t)=0, & x\in\partial\Omega,\;t\geq 0,\\ u(x,0)=u_0(x), \quad u_t(x,0)=u_1(x), & x\in \Omega,\end{matrix} \] where \[ Au=M\left(\|B^{1/2}u\|^2\right)e^{-\phi(x)} \text{div}(e^{\phi(x)}\nabla u), \] \[ \|B^{1/2}u\|^2 = \int_\Omega e^{\Phi(x)}|\nabla u|^2 dx, \] \(p > 2\) is a constant, \(k\) is a positive constant, \(M: \mathbb{R}^+\to \mathbb{R}^+\) is a continuous function, \(\Phi\in L^\infty(\Omega)\), and \(\Omega\subset\mathbb{R}^n\) is a bounded domain with a smooth boundary.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 1780544
zbMATH Keywords: blowup result
zbMATH Keywords: initial-boundary value problem
MaRDI profile type: Publication
OpenAlex ID: W1975088587
description: scientific article; zbMATH DE number 1780544