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Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains



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Arrieta Algarra, José María and Cholewa, Jan W. and Dlotko, Tomasz and Rodríguez Bernal, Aníbal (2004) Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains. Nonlinear Analysis: Theory, Methods & Applications, 56 (4). 515 – 554. ISSN 0362-546X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X03003808


In this paper we give general and flexible conditions for a reaction diffusion equation to be dissipative in an-unbounded domain. The functional setting is based on standard Lebesgue and Sobolev-Lebesgue spaces. We show how the reaction and diffusion mechanisms have to work together to obtain the asymptotic compactness of solutions and therefore the existence of the compact attractor. In particular cases, our results allow us to improve some previous known results.

Item Type:Article
Uncontrolled Keywords:Dissipativity; Attractors; Asymptotic behavior; Reaction-diffusion; Assymptotic compactness; Unbounded domains; Semilinear parabolic equations; Nonlinear boundary-conditions; Heat-equations; Blow-up; Schrodinger operator; Evolution-equations; Global attractor; Existence; Semigroups; Systems
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:18046
Deposited On:30 Jan 2013 09:37
Last Modified:12 Dec 2018 15:07

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