Differential and Integral Equations

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

Eduard Feireisl

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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


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