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Hyperbolic Equations in Uniform Spaces

J. W. Cholewa, Tomasz Dlotko (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space H ̇ ¹ l u ( ) × L ̇ ² l u ( ) . Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.

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