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Dynamics in dumbbell domains. II: The limiting problem

Arrieta Algarra, José María and Carvalho, Alexandre N. and Lozada-Cruz, Germán (2009) Dynamics in dumbbell domains. II: The limiting problem. Journal of Differential Equations, 247 (1). 174-202 . ISSN 0022-0396

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Abstract

In this work we continue the analysis of the asymptotic dynamics of reaction–diffusion problems in a dumbbell domain started in [J.M. Arrieta, A.N. Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551–597]. Here we study the limiting problem, that is, an evolution problem in a “domain” which consists of an open, bounded and smooth set Ω⊂RN with a curve R0 attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Ω the evolution is independent of the evolution in R0 whereas in R0 the evolution depends on the evolution in Ω through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors.


Item Type:Article
Uncontrolled Keywords:Domain with attached curve; Linear and nonlinear semigroups
Subjects:Sciences > Mathematics > Differential equations
ID Code:13944
Deposited On:23 Nov 2011 12:42
Last Modified:06 Feb 2014 09:56

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