Differential and Integral Equations

Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains

M. M. Cavalcanti, V. N. Domingos Cavalcanti, and T. F. Ma

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations Volume 17, Number 5-6 (2004), 495-510.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060344

Mathematical Reviews number (MathSciNet)
MR2054931

Zentralblatt MATH identifier
1174.74320

Subjects
Primary: 74D05: Linear constitutive equations
Secondary: 35B40: Asymptotic behavior of solutions 35R10: Partial functional-differential equations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 74H40: Long-time behavior of solutions 74K10: Rods (beams, columns, shafts, arches, rings, etc.)

Citation

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Ma, T. F. Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains. Differential Integral Equations 17 (2004), no. 5-6, 495--510. https://projecteuclid.org/euclid.die/1356060344.


Export citation