descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2014 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 47, pages 1,530-1,561 (issn: 0036-1410, eissn: 1095-7154,

Authors: Coti Zelati, Michele; Kalita, Piotr;

doi: 10.1137/140978995 , 10.48550/arxiv.1407.6135

arXiv: 1407.6135

Minimality Properties of Set-Valued Processes and their Pullback Attractors

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Abstract

We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties with respect to the notion of pullback attraction. When invariance is required, a very weak closed graph condition on the solving operators is assumed. The presentation is complemented with examples and counterexamples to test the sharpness of the hypotheses involved, including a reaction-diffusion equation, a discontinuous ordinary differential equation and an irregular form of the heat equation.

33 pages. A few typos corrected

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Keywords

closed graph condition, Topological dynamics of nonautonomous systems, Dynamical Systems (math.DS), PDEs with multivalued right-hand sides, nonautonomous parabolic problems, Mathematics - Analysis of PDEs, FOS: Mathematics, Attractors, Mathematics - Dynamical Systems, General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations, Analysis of PDEs (math.AP)

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