Premium
Global existence and uniform stability of solutions for a quasilinear viscoelastic problem
Author(s) -
Messaoudi Salim A.,
Tatar Nassereddine
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.804
Subject(s) - viscoelasticity , mathematics , stability (learning theory) , dirichlet boundary condition , mathematical analysis , nonlinear system , term (time) , boundary value problem , boundary (topology) , set (abstract data type) , wave equation , dirichlet distribution , dirichlet problem , computer science , physics , machine learning , thermodynamics , quantum mechanics , programming language
In this paper the nonlinear viscoelastic wave equation in canonical formwith Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd.