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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
DOI: https://doi.org/10.1090/S0002-9939-05-08340-1
Published electronically: 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 [Enhancements On Off] (What's this?)

  • 1. L. Dung, B. Nicolaenko, Exponential attractors in Banach spaces, J. Dynam. Differential Equations 13 (2001), 791-806. MR 1860286 (2002h:37158)
  • 2. A. Eden, C. Foias, B. Nicolaenko, R. Temam, Exponential attractors for dissipative evolution equations, Masson, Paris, 1994. MR 1335230 (96i:34148)
  • 3. M. Efendiev, A. Miranville, S. Zelik, Exponential attractors for a nonlinear reaction-diffusion system in $\mathbb{R} ^3$, C.R. Acad. Sci. Paris Sér. I Math. 330 (2000), 713-718. MR 1763916 (2001c:35039)
  • 4. 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)
  • 5. 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)
  • 6. 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
  • 7. 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
  • 8. 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.
  • 9. L.A. Lyusternik, M.I. Vishik, Regular degeneration and boundary layer for linear differential equations with small parameter, Trans. Amer. Math. Soc. 20 (1962), 239-364.
  • 10. A. Miranville, S. Zelik, Robust exponential attractors for Cahn-Hilliard type equations with singular potentials, Math. Methods Appl. Sci. 27 (2004), 545-582. MR 2041814 (2005b:37191)
  • 11. R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York, 1988. MR 0953967 (89m:58056)

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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: https://doi.org/10.1090/S0002-9939-05-08340-1
Keywords: Strongly continuous semigroups, robust exponential attractors, fractal dimension
Received by editor(s): December 14, 2003
Published electronically: August 22, 2005
Additional Notes: This research was partially supported by the Italian MIUR FIRB Research Project 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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