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Dynamics in dumbbell domains III. Continuity of attractors

Arrieta Algarra, José María and Carvalho, Alexandre N. and Lozada-Cruz, Germán (2009) Dynamics in dumbbell domains III. Continuity of attractors. Journal of Differential Equations, 247 (1). pp. 225-259. ISSN 0022-0396

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Abstract

In this paper we conclude the analysis started in [3] and continued in [4] con-
cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [4], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in Lp and H1 norms


Item Type:Article
Uncontrolled Keywords:Hyperbolic equilibria; Shrinking channels; Lower semicontinuous
Subjects:Sciences > Mathematics > Differential equations
ID Code:13945
Deposited On:23 Nov 2011 12:40
Last Modified:06 Feb 2014 09:56

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