On wave equation: review and recent results
type: Item
instance of: scholarly article
title: On wave equation: review and recent results
zbMATH Open document ID: 1395.35134
author: Ala A. Talahmeh
author: Salim A. Messaoudi
published in: Arabian Journal of Mathematics
publication date: 2018-06-01T00:00:00Z
review text: The first part of the article is devoted to a short review of some results on initial-boundary value problems for different kinds of nonlinear wave equations, pointing out authors own achievements. In the second part one remembers the definitions of variable-exponent Lebesgue and Sobolev spaces and shows the existence of a unique weak solution and a decay result to a specific IBV problem for the wave equation with nonlinear damping. Numerical applications for polynomial as well as exponential decay are discussed. Article ends with a blowup result to another IBV problem for a wave equation with nonlinear damping.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6879953
zbMATH Keywords: decay
zbMATH Keywords: blowup
zbMATH Keywords: nonlinear wave equations
zbMATH Keywords: variable-exponent Lebesgue and Sobolev spaces
zbMATH Keywords: nonlinear damping
MaRDI profile type: Publication
full work available at URL: s40065-017-0190-4
OpenAlex ID: W2770034798
Wikidata QID: Q59481443
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On wave equation: review and recent results (DOI)
DOI: 10.1007/S40065-017-0190-4