On the benefit of different additional regularity for the weakly coupled systems of semilinear effectively damped waves
type: Item
instance of: scholarly article
title: On the benefit of different additional regularity for the weakly coupled systems of semilinear effectively damped waves
zbMATH Open document ID: 1395.35140
author: Abdelhamid Mohammed Djaouti
published in: Mediterranean Journal of Mathematics
publication date: 2018-07-24T00:00:00Z
review text: The article refers to the classical Cauchy problem for a system of weakly coupled semilinear damped wave equations with time-dependent coefficients in the dissipation terms and power nonlinearities, with exponents \(p\) and \(q\). Under some assumptions on the exponents \(p\), \(q\), dissipation term coefficient and specific regularity conditions on data, one proves the existence of a uniquely determined globally -- in time -- Sobolev solution to the considered system, solution that satisfies certain decay estimates. In a special case, Sobolev solutions become energy solutions and additionally new estimates are proved. The two results in paper are similar and correspond to different choice of parameter.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L52
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6909954
zbMATH Keywords: weakly coupled hyperbolic systems
zbMATH Keywords: damped wave equations
zbMATH Keywords: global existence
zbMATH Keywords: \(L^2\)-decay
zbMATH Keywords: effective dissipation
zbMATH Keywords: small data solutions
MaRDI profile type: Publication
full work available at URL: s00009-018-1173-1
OpenAlex ID: W2804254472
cites work: Semi-linear wave equations with effective damping
cites work: Q3104370
cites work: Weakly coupled systems of semilinear effectively damped waves with time-dependent coefficient, different power nonlinearities and different regularity of the data
cites work: Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations
cites work: Critical exponent for the Cauchy problem to the weakly coupled damped wave system
cites work: Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping
cites work: Wave equations with time-dependent dissipation. II: Effective dissipation
Wikidata QID: Q129814479
DOI: 10.1007/S00009-018-1173-1
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description: scientific article; zbMATH DE number 6909954