Exponential attractors for non-autonomous dissipative system
EFENDIEV, Messoud ; YAMAMOTO, Yoshitaka ; YAGI, Atsushi
J. Math. Soc. Japan, Tome 63 (2011) no. 2, p. 647-673 / Harvested from Project Euclid
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In this paper we will introduce a version of exponential attractor for non-autonomous equations as a time dependent set with uniformly bounded finite fractal dimension which is positively invariant and attracts every bounded set at an exponential rate. This is a natural generalization of the existent notion for autonomous equations. A generation theorem will be proved under the assumption that the evolution operator is a compact perturbation of a contraction. In the second half of the paper, these results will be applied to some non-autonomous chemotaxis system.
Publié le : 2011-04-15
Classification:  exponential attractors,  non-autonomous dynamical system,  chemotaxis model,  37L25,  35K57 
@article{1303737800,
     author = {EFENDIEV, Messoud and YAMAMOTO, Yoshitaka and YAGI, Atsushi},
     title = {Exponential attractors for non-autonomous dissipative system},
     journal = {J. Math. Soc. Japan},
     volume = {63},
     number = {2},
     year = {2011},
     pages = { 647-673},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303737800}
}

EFENDIEV, Messoud; YAMAMOTO, Yoshitaka; YAGI, Atsushi. Exponential attractors for non-autonomous dissipative system. J. Math. Soc. Japan, Tome 63 (2011) no. 2, pp.  647-673. http://gdmltest.u-ga.fr/item/1303737800/