Differential and Integral Equations

Long-time behavior for a plate equation with nonlocal weak damping

M.A. Jorge Silva and V. Narciso

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 9/10 (2014), 931-948.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1404230051

Mathematical Reviews number (MathSciNet)
MR3229097

Zentralblatt MATH identifier
1340.35224

Subjects
Primary: 35L75: Nonlinear higher-order hyperbolic equations 35B40: Asymptotic behavior of solutions 35B41: Attractors

Citation

Silva, M.A. Jorge; Narciso, V. Long-time behavior for a plate equation with nonlocal weak damping. Differential Integral Equations 27 (2014), no. 9/10, 931--948. https://projecteuclid.org/euclid.die/1404230051


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