Communications on Pure and Applied Analysis (CPAA)

Semilinear damped wave equation in locally uniform spaces

Pages: 1673 - 1695, Volume 16, Issue 5, September 2017      doi:10.3934/cpaa.2017080

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Martin Michálek - Institute of Mathematics of the Czech Academy of Sciences, Prague, Žitná 25, 115 67 Praha 1, Czech Republic (email)
Dalibor Pražák - Charles University in Prague, Faculty of Mathematics and Physics, Dept. of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic (email)
Jakub Slavík - Department of Mathematical Analysis, Charles University, Prague, Sokolovská 83, 186 75 Praha 8, Czech Republic (email)

Abstract: We study a damped wave equation with a nonlinear damping in the locally uniform spaces and prove well-posedness and existence of a locally compact attractor. An upper bound on the Kolmogorov's $\varepsilon$-entropy is also established using the method of trajectories.

Keywords:  Damped wave equations, nonlinear damping, unbounded domains, locally compact attractor, Kolmogorov's entropy.
Mathematics Subject Classification:  Primary: 37L30; Secondary: 35B41, 35L70.

Received: September 2016;      Revised: March 2017;      Available Online: May 2017.