Existence and uniform decay for a non-linear viscoelastic equation with strong damping

Authors
Cavalcanti, MM Cavalcanti, VND Ferreira, J
Citation
Mm. Cavalcanti et al., Existence and uniform decay for a non-linear viscoelastic equation with strong damping, MATH METH A, 24(14), 2001, pp. 1043-1053
Citations number
11
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN journal
01704214 → ACNP
Volume
24
Issue
14
Year of publication
2001
Pages
1043 - 1053
Database
ISI
SICI code
0170-4214(20010925)24:14<1043:EAUDFA>2.0.ZU;2-6
Abstract
This paper is concerned with the non-linear viscoelastic equation \u(t)\(rho)u(n) - Deltau - Deltau(u) + integral (0)' g(t - tau) Deltau(tau )d tau - gamma Deltau(t) = 0 We prove global existence of weak solutions. Furthermore, uniform decay rat es of the energy are obtained assuming a strong damping Aut acting in the d omain and provided the relaxation function decays exponentially. Copyright (C) 2001 John Wiley & Sons, Ltd.