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References (31)
-
L. Medeiros, M. Miranda (1986)
Weak solutions for a system of nonlinear Klein-Gordon equationsAnnali di Matematica Pura ed Applicata, 146
-
Fuqin Sun, Mingxin Wang (2005)
Non-existence of global solutions for nonlinear strongly damped hyperbolic systemsDiscrete and Continuous Dynamical Systems, 12
-
Jian Zhang (2003)
On the standing wave in coupled non‐linear Klein–Gordon equationsMathematical Methods in the Applied Sciences, 26
-
V. Georgiev, G. Todorova (1994)
Existence of a Solution of the Wave Equation with Nonlinear Damping and Source TermsJournal of Differential Equations, 109
-
A. Haraux, E. Zuazua (1988)
Decay estimates for some semilinear damped hyperbolic problemsArchive for Rational Mechanics and Analysis, 100
-
S. Messaoudi (2008)
General decay of solutions of a viscoelastic equationJournal of Mathematical Analysis and Applications, 341
-
S. Messaoudi, N. Tatar (2007)
Global existence and uniform stability of solutions for a quasilinear viscoelastic problemMathematical Methods in the Applied Sciences, 30
-
M. Aassila, M. Cavalcanti, J. Soriano (2000)
Asymptotic Stability and Energy Decay Rates for Solutions of the Wave Equation with Memory in a Star-Shaped DomainSIAM J. Control. Optim., 38
-
W.J. Liu (1998)
The exponential stabilization of the higher-dimensional linear system of thermoviscoelasticityJ. Math. Pures Appl., 37
-
A. Mognon, D. Andrade (2003)
Global Solutions for a System of Klein-Gordon Equations with Memory - doi: 10.5269/bspm.v21i1-2.7512, 21
-
E. Zuazua (1990)
Exponential Decay for The Semilinear Wave Equation with Locally Distributed DampingCommunications in Partial Differential Equations, 15
-
Fuqin Sun, Mingxin Wang (2006)
Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms☆Nonlinear Analysis-theory Methods & Applications, 64
-
M. Cavalcanti, H. Oquendo (2003)
Frictional versus Viscoelastic Damping in a Semilinear Wave EquationSIAM J. Control. Optim., 42
-
Weijiu Liu (1998)
The exponential stabilization of the higher-dimensional linear system of thermoviscoelasticityJournal de Mathématiques Pures et Appliquées, 77
-
M. Cavalcanti, V. Cavalcanti, J. Filho, J. Soriano (2001)
Existence and uniform decay rates for viscoelastic problems with nonlinear boundary dampingDifferential and Integral Equations
-
T. Shardlow (2002)
A coupled Cahn-Hilliard particle systemElectronic Journal of Differential Equations, 2002
-
Wenjun Liu, Mingxin Wang (2008)
Blow-up of the Solution for a p-Laplacian Equation with Positive Initial EnergyActa Applicandae Mathematicae, 103
-
I. Segal (1963)
The global Cauchy problem for a relativistic scalar field with power interactionBulletin de la Société Mathématique de France, 91
-
S. Messaoudi, N. Tatar (2008)
Exponential and polynomial decay for a quasilinear viscoelastic equationNonlinear Analysis-theory Methods & Applications, 68
-
D. Andrade, A. Mognon (2003)
Global solutions for a system of Klein–Gordon equations with memoryBol. Soc. Paran. Mat. Ser. 3, 21
-
G. Milton, V. Nesi (1999)
Optimal G-Closure Bounds¶via Stability under LaminationArchive for Rational Mechanics and Analysis, 150
-
S. Messaoudi, N. Tatar (2008)
Uniform stabilization of solutions of a nonlinear system of viscoelastic equationsApplicable Analysis, 87
-
H.A. Levine (1974)
Instability and nonexistence of global solutions of nonlinear wave equation of the form Pu tt =Au+F(u)Trans. Am. Math. Soc., 192
-
Xiaosen Han, Mingxin Wang (2009)
General decay of energy for a viscoelastic equation with nonlinear dampingMathematical Methods in the Applied Sciences, 32
-
S. Messaoudi (2008)
General decay of the solution energy in a viscoelastic equation with a nonlinear sourceNonlinear Analysis-theory Methods & Applications, 69
-
H. Levine, J. Serrin (1997)
Global Nonexistence Theorems for Quasilinear Evolution Equations with DissipationArchive for Rational Mechanics and Analysis, 137
-
Enzo Vitillaro (1999)
Global Nonexistence Theorems for a Class of Evolution Equations with DissipationArchive for Rational Mechanics and Analysis, 149
-
H. Levine (1974)
Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations -
M. Santos (2002)
Decay rates for solutions of a system of wave equations with memory, 2002
-
M. Cavalcanti, V. Cavalcanti, J. Ferreira (2001)
Existence and uniform decay for a non‐linear viscoelastic equation with strong dampingMathematical Methods in the Applied Sciences, 24
-
Fatiha Alabau-Boussouira, P. Cannarsa, D. Sforza (2008)
Decay estimates for second order evolution equations with memoryJournal of Functional Analysis, 254
- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-008-9391-3
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we consider a system of two coupled viscoelastic equations with Dirichlet boundary condition which describes the interaction between two different fields arising in viscoelasticity. For certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation functions which is not necessarily of exponential or polynomial type. This result improves earlier one of Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and extends some existing results concerning the general decay for a single equation to the case of a system.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Nov 28, 2008