Open Access
Translator Disclaimer
2004 Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains
M. M. Cavalcanti, V. N. Domingos Cavalcanti, T. F. Ma
Differential Integral Equations 17(5-6): 495-510 (2004).

Abstract

The viscoelastic Euler-Bernoulli equation with nonlinear and nonlocal damping $$u_{tt}+\Delta^2u-\int_0^tg(t-\tau )\Delta^2u(\tau )\,d\tau +a(t )u_t=0\,\,\,\hbox{in}\,\,\,\Omega\times {\bf R}^{+},$$ where $a(t)=M\left(\int_{\Omega}\left|\nabla u(x,t)\right|^2dx\right )$, is considered in bounded or unbounded domains $\Omega$ of ${\bf R}^ n$. The existence of global solutions and decay rates of the energy are proved.

Citation

Download Citation

M. M. Cavalcanti. V. N. Domingos Cavalcanti. T. F. Ma. "Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains." Differential Integral Equations 17 (5-6) 495 - 510, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1174.74320
MathSciNet: MR2054931

Subjects:
Primary: 74D05
Secondary: 35B40 , 35R10 , 45K05 , 74H40 , 74K10

Rights: Copyright © 2004 Khayyam Publishing, Inc.

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.17 • No. 5-6 • 2004
Back to Top