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A construction of a robust family of exponential attractors
Authors:
Stefania Gatti, Maurizio Grasselli, Alain Miranville and Vittorino Pata
Journal:
Proc. Amer. Math. Soc. 134 (2006), 117-127
MSC (2000):
Primary 37L25, 37L30
Posted:
August 22, 2005
MathSciNet review:
2170551
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Abstract: Given a dissipative strongly continuous semigroup depending on some parameters, we construct a family of exponential attractors which is robust, in the sense of the symmetric Hausdorff distance, with respect to (even singular) perturbations.
References
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A. Eden, C. Foias, B. Nicolaenko, R. Temam, Exponential attractors for dissipative evolution equations, Masson, Paris, 1994. MR 1335230 (96i:34148)
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M. Efendiev, A. Miranville, S. Zelik, Exponential attractors for a nonlinear reaction-diffusion system in
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M. Efendiev, A. Miranville, S. Zelik, Exponential attractors for a singularly perturbed Cahn-Hilliard system, Math. Nachr. 272 (2004), 11-31. MR 2079758 (2005h:37195)
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M. Efendiev, A. Miranville, S. Zelik, Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A 134, (2004), 271-315. MR 2056285 (2005h:37196)
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P. Fabrie, C. Galusinski, A. Miranville, S. Zelik, Uniform exponential attractors for a singularly perturbed damped wave equation, Discrete Contin. Dynam. Systems 10 (2004), 211-238. MR 2026192
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S. Gatti, M. Grasselli, A. Miranville, V. Pata, Hyperbolic relaxation of the viscous Cahn-Hilliard equation in 3-D, Math. Models Methods Appl. Sci., 15 (2005), 165-198. MR 2119676
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M. Grasselli, A. Miranville, V. Pata, S. Zelik, Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. To appear in Mathematische Nachrichten.
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Additional Information
Stefania Gatti
Affiliation:
Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, I-44100 Ferrara, Italy
Email:
s.gatti@economia.unife.it
Maurizio Grasselli
Affiliation:
Dipartimento di Matematica ``F.Brioschi'', Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy
Email:
maugra@mate.polimi.it
Alain Miranville
Affiliation:
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France
Email:
miranv@math.univ-poitiers.fr
Vittorino Pata
Affiliation:
Dipartimento di Matematica ``F.Brioschi'', Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy
Email:
pata@mate.polimi.it
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08340-1
PII:
S 0002-9939(05)08340-1
Keywords:
Strongly continuous semigroups,
robust exponential attractors,
fractal dimension
Received by editor(s):
December 14, 2003
Posted:
August 22, 2005
Additional Notes:
This research was partially supported by the Italian MIUR FIRB Research Project {\it Analisi di Equazioni a Derivate Parziali, Lineari e Non Lineari: Aspetti Metodologici, Modellistica, Applicazioni}
Communicated by:
David S. Tartakoff
Article copyright:
© Copyright 2005 American Mathematical Society
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