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Global Existence and Uniform Decay of Solutions for a Coupled System of Nonlinear Viscoelastic Wave Equations with Not Necessarily Differentiable Relaxation Functions
Author(s) -
Liu W.,
Yu J.
Publication year - 2011
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2011.00524.x
Subject(s) - relaxation (psychology) , nonlinear system , viscoelasticity , differentiable function , mathematics , mathematical analysis , boundary value problem , energy method , exponential decay , exponential function , galerkin method , wave equation , physics , thermodynamics , psychology , social psychology , quantum mechanics , nuclear physics
In this paper, we consider the initial boundary value problem for a coupled system of nonlinear viscoelastic wave equations with source terms. By using the Faedo–Galerkin method, potential well theory and perturbed energy technique, we establish the global existence and exponential decay of solutions under weaker conditions on the relaxation functions that are not necessarily differentiable.