General decay of solutions of a nonlinear system of viscoelastic wave equations

Handle URI:
http://hdl.handle.net/10754/561755
Title:
General decay of solutions of a nonlinear system of viscoelastic wave equations
Authors:
Said-Houari, Belkacem; Messaoudi, Salim A.; Guesmia, Aïssa
Abstract:
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Verlag
Journal:
Nonlinear Differential Equations and Applications
Issue Date:
16-Apr-2011
DOI:
10.1007/s00030-011-0112-7
Type:
Article
ISSN:
10219722
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSaid-Houari, Belkacemen
dc.contributor.authorMessaoudi, Salim A.en
dc.contributor.authorGuesmia, Aïssaen
dc.date.accessioned2015-08-03T09:03:52Zen
dc.date.available2015-08-03T09:03:52Zen
dc.date.issued2011-04-16en
dc.identifier.issn10219722en
dc.identifier.doi10.1007/s00030-011-0112-7en
dc.identifier.urihttp://hdl.handle.net/10754/561755en
dc.description.abstractThis work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.en
dc.publisherSpringer Verlagen
dc.subjectGeneral decayen
dc.subjectNonlinear sourceen
dc.subjectViscoelastic dampingen
dc.titleGeneral decay of solutions of a nonlinear system of viscoelastic wave equationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalNonlinear Differential Equations and Applicationsen
dc.contributor.institutionLaboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac, Franceen
dc.contributor.institutionDepartment of Mathematics and Statistics KFUPM, Dhahran 31261, Saudi Arabiaen
dc.contributor.institutionLMAM, Bat. A, Université Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz Cedex 01, Franceen
kaust.authorSaid-Houari, Belkacemen
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