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arXiv · 1304.2903

Totally dissipative dynamical processes and their uniform global attractors

Vladimir V. Chepyzhov·Monica Conti·Vittorino Pata
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Abstract

We discuss the existence of the global attractor for a family of processes $U_\sigma(t,\tau)$ acting on a metric space $X$ and depending on a symbol $\sigma$ belonging to some other metric space $\Sigma$. Such an attractor is uniform with respect to $\sigma\in\Sigma$, as well as with respect to the choice of the initial time $\tau\in\R$. The existence of the attractor is established for totally dissipative processes without any continuity assumption. When the process satisfies some additional (but rather mild) continuity-like hypotheses, a characterization of the attractor is given.

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Vladimir V. Chepyzhov, Monica Conti, Vittorino Pata. 2013-04-10. Totally dissipative dynamical processes and their uniform global attractors. https://arxiv.org/abs/1304.2903

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