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New generalizations of the Cahn-Hilliard equation based on a microforce balance

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Analysis and Simulation of Multifield Problems

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 12))

Abstract

In this article, we further generalize the models of Cahn-Hilliard equations proposed by M. Gurtin and based on a balance law for microforces. These models are consistent with the second law of thermodynamics. We also discuss the existence and uniqueness of solutions.

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References

  1. Cahn, J. W. (1961) On spinodal decomposition, Acta Metall. 9. 795–801.

    Article  Google Scholar 

  2. Cahn, J. W., Hilliard, J. E. (1958) Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys. 2, 258–267.

    Google Scholar 

  3. Fried, E., Gurtin, M. (1994) Dynamic solid-solid phase transitions with phase characterized by an order parameter, Physica D 72, 287–308.

    Article  MathSciNet  MATH  Google Scholar 

  4. Gajewski, H., Zacharias, K. (2001) On a nonlocal phase separation model, Preprint.

    Google Scholar 

  5. Giacomin, G., Lebowitz, J. L. (1997) Phase segregation dynamics in particle systems with long range interaction I. Macroscopic limits, J. Statist. Phys. 87. 37–61.

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  6. Gurtin, M. (1996) Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92, 178–192.

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  7. Miranville, A. (2000) Some generalizations of the Cahn-Hilliard equation, Asymptotic Anal. 22, 235–259.

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  8. Miranville, A. (2001) Long-time behavior of some models of Cahn-Hilliard equations in deformable continua, Nonlinear Anal. Ser. B 2, 273–304.

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  9. Miranville, A. (2001) Consistent models of Cahn-Hilliard-Gurtin equations with Neumann boundary conditions, Physica D 158, 233–257.

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  10. In preparation.

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Author information

Authors and Affiliations

  1. Laboratoire d’Applications des Mathématiques, SP2MI, Téléport 2, Université de Poitiers, Avenue Marie et Pierre Curie, 86962, Chasseneuil Futuroscope Cedex, France

    Alain Miranville

  2. Fakultät Mathematik, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Messoud Efendiev

Authors
  1. Alain Miranville
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  2. Messoud Efendiev
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik, Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Wolfgang Wendland  & Messoud Efendiev  & 

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© 2003 Springer-Verlag Berlin Heidelberg

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Miranville, A., Efendiev, M. (2003). New generalizations of the Cahn-Hilliard equation based on a microforce balance. In: Wendland, W., Efendiev, M. (eds) Analysis and Simulation of Multifield Problems. Lecture Notes in Applied and Computational Mechanics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36527-3_27

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  • DOI: https://doi.org/10.1007/978-3-540-36527-3_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05633-8

  • Online ISBN: 978-3-540-36527-3

  • eBook Packages: Springer Book Archive

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