Open Access
Translator Disclaimer
2002 Global existence and asymptotic stability for viscoelastic problems
M. M. Cavalcanti, V. N. Domingos Cavalcanti, T. F. Ma, J. A. Soriano
Differential Integral Equations 15(6): 731-748 (2002).

Abstract

One considers the damped semilinear viscoelastic wave equation $$u_{tt}-\Delta u+\alpha u+f(u)+\int_0^tg(t-\tau )\Delta u(\tau )\, d\tau +h(u_t)=0\,\,\,\hbox{in}\,\,\,\Omega\times (0,\infty ),$$ where $\Omega$ is any bounded or finite measure domain of ${\bf R}^ n$, $\alpha\geq 0$ and $f,h$ are power like functions. The existence of global regular and weak solutions is proved by means of the Faedo-Galerkin method and uniform decay rates of the energy are obtained following the perturbed energy method by assuming that $g$ decays exponentially.

Citation

Download Citation

M. M. Cavalcanti. V. N. Domingos Cavalcanti. T. F. Ma. J. A. Soriano. "Global existence and asymptotic stability for viscoelastic problems." Differential Integral Equations 15 (6) 731 - 748, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1015.35071
MathSciNet: MR1893844

Subjects:
Primary: 74H20
Secondary: 35B35 , 35B40 , 35L70 , 35Q72 , 74D10 , 74H25 , 74H40

Rights: Copyright © 2002 Khayyam Publishing, Inc.

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.15 • No. 6 • 2002
Back to Top