On the connectedness and asymptotic behaviour of solutions of reaction–diffusion systems☆
By José Valero, Alexey V. Kapustyan. 2006
79 citations recorded by the source corpus.
Abstract In this paper we consider reaction–diffusion systems in which the conditions imposed on the nonlinearity provide global existence of solutions of the Cauchy problem, but not uniqueness. We prove first that for the set of all weak solutions the Kneser property holds, that is, that the set of values attained by the solutions at every moment of time is compact and connected. Further, we prove the existence and connectedness of a global attractor in both the autonomous and nonautonomous cases. The obtained results are applied to several models of physical (or chemical) interest: a model of fractional-order chemical autocatalysis with decay, the Fitz–Hugh–Nagumo equation and the Ginzburg–Landau equation.
Subfields: Computer Networks and Communications, Control and Systems Engineering, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/5ee51967acba2b7a8726a40f8abe8f21391b6864
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In Computer Networks and Communications
In Control and Systems Engineering
In Modeling and Simulation
Citations in the corpus
- Structure and regularity of the global attractor of a reaction-di{\S}usion equation with non-smooth nonlinear term (2012, background): “Such equation generates in the general case a multivalued semiflow having a global compact attractor (see [10], [14], [17], [29]).”