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RESEARCH PRODUCT

On the Kneser property for reaction–diffusion equations in some unbounded domains with an -valued non-autonomous forcing term

María AnguianoJosé ValeroFrancisco Morillas

subject

Forcing (recursion theory)Social connectednessApplied MathematicsMathematical analysisPoincaré inequalityPullback attractorSpace (mathematics)Domain (mathematical analysis)symbols.namesakeReaction–diffusion systemsymbolsLogistic functionAnalysisMathematics

description

Abstract In this paper, we prove the Kneser property for a reaction–diffusion equation on an unbounded domain satisfying the Poincare inequality with an external force taking values in the space H − 1 . Using this property of solutions we check also the connectedness of the associated global pullback attractor. We study also similar properties for systems of reaction–diffusion equations in which the domain is the whole R N . Finally, the results are applied to a generalized logistic equation.

yearjournalcountryeditionlanguage
2012-03-01Nonlinear Analysis: Theory, Methods & Applications
https://doi.org/10.1016/j.na.2011.11.007