Affiliation:
1. Institut Elie Cartan de Lorraine, UMR 7502, Université de Lorraine, 3 Rue Augustin Fresnel, BP 45112, 57073 Metz Cedex 03, France
Abstract
We consider in this paper the problem of asymptotic behavior of solutions for two viscoelastic
wave equations with infinite memory. We show that the stability of the system holds for a much larger class of kernels
and get better decay rate than the ones known in the literature. More precisely, we consider infinite memory kernels
satisfying, where and are given functions. Under this very general assumption on the behavior of g at infinity and for
each viscoelastic wave equation, we provide a relation between the decay rate of the solutions and the growth of g at
infinity, which improves the decay rates obtained in [15, 16, 17, 19, 40]. Moreover, we drop the boundedness assumptions
on the history data considered in [15, 16, 17, 40].
Publisher
Vilnius Gediminas Technical University
Subject
Modelling and Simulation,Analysis
Reference40 articles.
1. ON EXPONENTIAL ASYMPTOTIC STABILITY IN LINEAR VISCOELASTICITY
2. Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping;S. Berrimi;Electronic Journal of Differential Equations,2004
3. Existence and uniform decay for a non-linear viscoelastic equation with strong damping
4. General decay rates of solutions to a nonlinear wave equation with boundary condition of memory type;M. Cavalcanti;Differential and Integral Equations,2005
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