## Differential and Integral Equations

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

#### 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