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A reaction-diffusion equation on a thin L-shaped domain

Published online by Cambridge University Press:  14 November 2011

Jack K. Hale  and
Geneviève Raugel
Jack K. Hale
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
Geneviève Raugel
Affiliation:
Laboratoire d'Analyse Numérique, Bâtiment 425, Université Paris-Sud, 91405 Orsay cédex, France
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Abstract

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We consider a dissipative reaction–diffusion equation on a thin L-shaped domain (with the thinness measured by a parameter ε); we determine the limit equation for ε = 0 and prove the upper semicontinuity of the global attractors at ε = 0. We also state a lower semicontinuity result. When the limit equation is one-dimensional, we prove convergence of any orbit to a singleton.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 2 , 1995 , pp. 283 - 327
Copyright
Copyright © Royal Society of Edinburgh 1995

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