On the connectedness and asymptotic behaviour of solutions of reaction-diffusion systems |
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Authors: | José Valero,Alexey Kapustyan |
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Affiliation: | a Universidad Miguel Hernández, Centro de Investigación Operativa, Avda. de la Universidad, s/n, 03202 Elche, Alicante, Spain b Kiev National Taras Shevchenko University, 01033 Kiev, Ukraine |
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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. |
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Keywords: | Reaction-diffusion system Set-valued dynamical system Global attractor Kneser property |
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