Hyperbolic Equations in Uniform Spaces
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 249-263
MSC: 35L15, 35B40, 35B41.
DOI: 10.4064/ba52-3-5
Abstract
The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ${\mathbb R}^n$. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space $\dot H^1_{\rm lu}({\mathbb R}^n)\times \dot L^2_{\rm lu}({\mathbb R}^n)$. Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.
