Attractors and entropy bounds for a nonlinear RDEs with distributed delay in unbounded domains
Dalibor Pražák Jakub Slavík
A nonlinear reaction-diffusion problem with a general, both spatially and delay distributed reaction term is considered in an unbounded domain $\mathbb{R}^N$. The existence of a unique weak solution is proved. A locally compact attractor together with entropy bound is also established.
keywords: Kolmogorov's $\varepsilon$-enthropy. unbounded domain attractor Nonlinear reaction-diffusion equation distributed delay
Semilinear damped wave equation in locally uniform spaces
Martin Michálek Dalibor Pražák Jakub Slavík

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

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