Minimality properties of set-valued processes and their pullback attractors
Analysis of PDEs
2014-08-13 v2 Dynamical Systems
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.
Cite
@article{arxiv.1407.6135,
title = {Minimality properties of set-valued processes and their pullback attractors},
author = {Michele Coti Zelati and Piotr Kalita},
journal= {arXiv preprint arXiv:1407.6135},
year = {2014}
}
Comments
33 pages. A few typos corrected