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 . ).$
Citation
Eduard Feireisl. "Bounded, locally compact global attractors for semilinear damped wave equations on $\mathbb{R}^N$." Differential Integral Equations 9 (5) 1147 - 1156, 1996. https://doi.org/10.57262/die/1367871535
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