## Differential and Integral Equations

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367871535

**Mathematical Reviews number (MathSciNet)**

MR1392099

**Zentralblatt MATH identifier**

0858.35084

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

Secondary: 35B40: Asymptotic behavior of solutions 35L05: Wave equation 35L15: Initial value problems for second-order hyperbolic equations

#### Citation

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