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Dimension of Maximal Attractors for the m–dimensional Cahn–Hilliard System

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Abstract

On the basis of the existence of the maximal attractor of the m–dimensional Cahn–Hilliard system in the product spaces (L 2(Ω))m and (H 2(Ω))m, in this paper, its Hausdorff dimension is estimated by calculating the orthogonal projection of the linear variational operator of the system.

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References

  1. Cahn, J. W., Hilliard, J. E.: Free energy of a nonuniform system I. Interfacial free energy. J. Chem. Phys., 28, 258–267 (1958)

    Article  Google Scholar 

  2. Novick–Cohen, A., Segel, L. A.: Nonlinear aspects of the Cahn–Hilliard equation. Physica, 10D, 277–298 (1984)

    MathSciNet  Google Scholar 

  3. Temam, R.: Infinite–Dimensional Dynamical Systems in Mechanics and Physics, Springer–Verlag, New York, 1988

  4. Dlotko, T.: Global attractor for the Cahn–Hilliard equation in H 2 and H 3. J. Diff. Eqns., 113, 381–393 (1994)

    Article  MathSciNet  Google Scholar 

  5. Elliott, C. M., Luckhaus, S.: A generalized diffusion equation for phase separation of a multicomponent mixture with interfacial free energy, IMA, Preprint 887, 1991

  6. Eyre, D. J.: Systems of Cahn–Hilliard equations, University of Minnisota, AHPCRC Preprint 92–102, 1992

  7. Gao, W., Yin, J.: Systems of Cahn–Hilliard equations with density–dependent transition matrices. Chinese Ann. Math. Ser. A, 20, 169–176 (1999) (in Chinese)

    Article  MathSciNet  Google Scholar 

  8. Maier–Paape, S., Stoth, B., Wanner, T.: Spinodal decomposition for multicomponent Cahn–Hilliard systems. J. Statist. Phys., 98, 871–896 (2000)

    Article  MathSciNet  Google Scholar 

  9. Hale, J. K.: Asymptotic Behavior of Dissipative Systems, AMS, Providence, Rhode Island, 1988

  10. Cholewa, J. W., Dlotko, T.: Global attractor for the Cahn–Hilliard system. Bull. Austral. Math. Soc., 40, 277–293 (1993)

    MathSciNet  Google Scholar 

  11. Li, D., Zhong, C.: Global attractor for the Cahn–Hilliard system with fast growing nonlinearity. J. Diff. Eqns., 149, 191–210 (1998)

    Article  Google Scholar 

  12. Zhang, W.: Maximal attractors for the m–dimensional Cahn–Hilliard system. Acta Mathematica Sinica, English. Series, 20(2), 233–246 (2004)

    Article  MathSciNet  Google Scholar 

  13. Henry, D.: Geometric Theory of Semilinear Parabolic Equations, LN in Math., 840, Springer–Verlag, New York, 1981

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

    Wei Nian Zhang

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  1. Wei Nian Zhang
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Correspondence to Wei Nian Zhang.

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Supported by NSFC(China) grants #10471101 and #10428104, TRAPOYT and China MOE Doctoral Base Research Grant

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Zhang, W.N. Dimension of Maximal Attractors for the m–dimensional Cahn–Hilliard System. Acta Math Sinica 21, 1487–1494 (2005). https://doi.org/10.1007/s10114-005-0633-2

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  • DOI: https://doi.org/10.1007/s10114-005-0633-2

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