## Differential and Integral Equations

### Bounded, locally compact global attractors for semilinear damped wave equations on $\mathbb{R}^N$

Eduard Feireisl

#### Abstract

We prove the existence of a global attractor for the equation $$u_{tt} + u_t - \Delta u + f(u) = 0 ,\quad u= u(x,t) \ , \ x\in \mathbb{R}^N .$$ The attractor is compact in $H^1_{loc}(\mathbb{R}^N .) \times L^2_{loc}(\mathbb{R}^N . ).$

#### Article information

Source
Differential Integral Equations, Volume 9, Number 5 (1996), 1147-1156.

Dates
First available in Project Euclid: 6 May 2013

Feireisl, Eduard. Bounded, locally compact global attractors for semilinear damped wave equations on $\mathbb{R}^N$. Differential Integral Equations 9 (1996), no. 5, 1147--1156. https://projecteuclid.org/euclid.die/1367871535