Geodesic
Hyperbolic Equations in Uniform Spaces
J. W. Cholewa1 ; Tomasz Dlotko1
1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 249-263 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba52-3-5
Keywords: paper devoted cauchy problem semilinear damped wave equation whole mathbb under suitable assumptions bounded dissipative semigroup global solutions constructed locally uniform space dot mathbb times dot mathbb asymptotic compactness semigroup existence global attractor shown

J. W. Cholewa 1 ; Tomasz Dlotko 1

1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland 
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J. W. Cholewa; Tomasz Dlotko. Hyperbolic Equations in Uniform Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 249-263. doi: 10.4064/ba52-3-5

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