Uniform decay of solutions for a quasilinear system of viscoelastic equations

In this paper, we consider a system of two coupled quasilinear viscoelastic equations in canonical form with Dirichlet boundary condition. We use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay (with exponential and...

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Bibliographic Details
Published inNonlinear analysis Vol. 71; no. 5; pp. 2257 - 2267
Main Author Liu, Wenjun
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.09.2009
Elsevier
Subjects
Coupled viscoelastic equations
Exact sciences and technology
Exponential decay
Mathematical analysis
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Polynomial decay
Relaxation function
Sciences and techniques of general use
Uniform decay
35B37
93D20
Coupled viscoelastic equations
93D15
Uniform decay
Polynomial decay
Relaxation function
35L55
Exponential decay
Polynomial
Nonlinear analysis
Mathematical model
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Summary:In this paper, we consider a system of two coupled quasilinear viscoelastic equations in canonical form with Dirichlet boundary condition. We use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay (with exponential and polynomial rates) of the solutions energy, which extends some existing results for a single equation to the case of a coupled system.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.01.060