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September/October 2014 Long-time behavior for a plate equation with nonlocal weak damping
M.A. Jorge Silva, V. Narciso
Differential Integral Equations 27(9/10): 931-948 (September/October 2014).

Abstract

This paper is devoted to the long-time behavior of solutions for a class of plate equations with nonlocal weak damping $$ u_{tt} + \Delta^2 u + g(u) + M \Big (\int_{\Omega}|\nabla u|^2 dx \Big )u_t =f\quad \mbox{in} \quad \Omega\times\mathbb{R}^{+}, $$ where $\Omega$ is a bounded domain of $\mathbb{R}^N$. Under suitable conditions on the nonlinear forcing term $g(u)$ and Kirchhoff damping coefficient $M (\int|\nabla u|^2 ),$ the existence of a global attractor with finite Hausdorff and fractal dimensions is proved.

Citation

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M.A. Jorge Silva. V. Narciso. "Long-time behavior for a plate equation with nonlocal weak damping." Differential Integral Equations 27 (9/10) 931 - 948, September/October 2014.

Information

Published: September/October 2014
First available in Project Euclid: 1 July 2014

zbMATH: 1340.35224
MathSciNet: MR3229097

Subjects:
Primary: 35B40, 35B41, 35L75

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 9/10 • September/October 2014
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