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Global and exponential attractors for nonlinear reaction–diffusion systems in unbounded domains

Published online by Cambridge University Press:  12 July 2007

M. Efendiev ,
A. Miranville  and
S. Zelik
M. Efendiev
Affiliation:
Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
A. Miranville
Affiliation:
Université de Poitiers, Laboratoire d'Applications des Mathématiques–SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, 86962 Chasseneuil Futuroscope Cedex, France
S. Zelik
Affiliation:
Université de Poitiers, Laboratoire d'Applications des Mathématiques–SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, 86962 Chasseneuil Futuroscope Cedex, France
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Abstract

We study the long-time behaviour of solutions of autonomous and non-autonomous reaction-diffusion equations in unbounded domains of R3. It is shown that, under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess compact global (uniform) attractors in the corresponding phase space. Estimates for Kolmogorov's ε-entropy of these attractors in terms of Kolmogorov's entropy of the external forces are given. Moreover, (infinite-dimensional) exponential attractors with the same entropy estimate as that of the corresponding global (uniform) attractor are also constructed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 2 , April 2004 , pp. 271 - 315
Copyright
Copyright © Royal Society of Edinburgh 2004

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