Dissipative parabolic equations in locally uniform spaces



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Arrieta Algarra, José María and Cholewa, Jan W. and Dlotko, Tomasz and Rodríguez Bernal, Aníbal (2007) Dissipative parabolic equations in locally uniform spaces. Mathematische Nachrichten, 280 (15). pp. 1643-1663. ISSN 0025-584X

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.200510569/pdf


The Cauchy problem for a semilinear second order parabolic equation u(t) = Delta u + f (x, u, del u), (t, x) epsilon R+ x R-N, is considered within the semigroup approach in locally uniform spaces W-U(s,p) (R-N). Global solvability, dissipativeness and the existence of an attractor are established under the same assumptions as for problems in bounded domains. In particular, the condition sf (s, 0) < 0, |s| > s(0) > 0, together with gradient's "subquadratic" growth restriction, are shown to guarantee the existence of an attractor for the above mentioned equation. This result cannot be located in the previous references devoted to reaction-diffusion equations in the whole of R-N.

Item Type:Article
Uncontrolled Keywords:Cauchy problem in RN; Dissipativeness; Global attractor
Subjects:Sciences > Mathematics > Functions
ID Code:17699
Deposited On:16 Jan 2013 10:19
Last Modified:12 Dec 2018 15:07

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