Nonexistence of global solutions of nonlinear wave equations.
type: Item
instance of: scholarly article
title: Nonexistence of global solutions of nonlinear wave equations.
zbMATH Open document ID: 1101.35337
author: R. Eloulaimi
author: M. Guedda
published in: Portugaliae Mathematica. Nova Série
publication date: 2001-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/52870
full work available at URL: 6.html
review text: Summary: In this paper the nonexistence of global solutions to wave equations of the type \[ u_{tt}-\Delta u\pm u_t=\lambda\,u + | u|^{1+q} \] is considered. We derive, for an averaging of solutions, a nonlinear second order differential inequality of the type \(w^{\prime\prime} \pm w^\prime \geq b\,w + | w|^{1+q}\), and we prove a blowing up phenomenon under some restriction on \(u(x,0)\) and \(u_t(x,0)\). Similar results are given for other equations.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1975348
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1975348