We study the existence of attractors for partly dissipative systems in ℝⁿ. For these systems we prove the existence of global attractors with attraction properties and compactness in a slightly weaker topology than the topology of the phase space. We obtain abstract results extending the usual theory to encompass such two-topologies attractors. These results are applied to the FitzHugh-Nagumo equations in ℝⁿ and to Field-Noyes equations in ℝ. Some embeddings between uniformly local spaces are also proved.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-2-6,
author = {Alexandre N. Carvalho and Tomasz Dlotko},
title = {Partly dissipative systems in uniformly local spaces},
journal = {Colloquium Mathematicae},
volume = {100},
year = {2004},
pages = {221-242},
zbl = {1059.35017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-2-6}
}
Alexandre N. Carvalho; Tomasz Dlotko. Partly dissipative systems in uniformly local spaces. Colloquium Mathematicae, Tome 100 (2004) pp. 221-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-2-6/