Hyperbolic Equations in Uniform Spaces

Tom 52 / 2004

J. W. Cholewa, Tomasz Dlotko Bulletin Polish Acad. Sci. Math. 52 (2004), 249-263 MSC: 35L15, 35B40, 35B41. DOI: 10.4064/ba52-3-5

Streszczenie

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.

Autorzy

  • J. W. CholewaInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • Tomasz DlotkoInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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