6533b872fe1ef96bd12d420e

RESEARCH PRODUCT

On the Kneser property for reaction–diffusion systems on unbounded domains

Francisco MorillasJosé Valero

subject

Kneser propertyPure mathematicsProperty (philosophy)Social connectednessMathematical analysisSet-valued dynamical systemGlobal attractorUnbounded domainSet (abstract data type)Compact spaceReaction–diffusion systemReaction–diffusion systemAttractorInitial value problemGeometry and TopologyUniquenessMathematics

description

Abstract We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for reaction–diffusion systems on unbounded domains in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property we obtain that the global attractor of such systems is connected. Finally, these results are applied to the complex Ginzburg–Landau equation.

yearjournalcountryeditionlanguage
2009-12-01Topology and its Applications
https://doi.org/10.1016/j.topol.2009.03.049