Bi-spaces global attractors in abstract parabolic equations

J. W. Cholewa; T. Dłotko

Banach Center Publications, Tome 60 (2003), p. 13-26 / Harvested from The Polish Digital Mathematics Library

Résumé

An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on $X^{α}$ . This semigroup possesses an $(X^{α} - Z)$ -global attractor that is closed, bounded, invariant in $X^{α}$ , and attracts bounded subsets of $X^{α}$ in a ’weaker’ topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system.

Publié le : 2003-01-01

Zbl 1024.35058

EUDML-ID : urn:eudml:doc:281886

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     author = {J. W. Cholewa and T. D\l otko},
     title = {Bi-spaces global attractors in abstract parabolic equations},
     journal = {Banach Center Publications},
     volume = {60},
     year = {2003},
     pages = {13-26},
     zbl = {1024.35058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-1}
}

J. W. Cholewa; T. Dłotko. Bi-spaces global attractors in abstract parabolic equations. Banach Center Publications, Tome 60 (2003) pp. 13-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-1/