Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation

Martine Marion

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1989)

  • Volume: 23, Issue: 3, page 463-488
  • ISSN: 0764-583X

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Marion, Martine. "Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 23.3 (1989): 463-488. <http://eudml.org/doc/193573>.

@article{Marion1989,
author = {Marion, Martine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {phase transition; approximate inertial manifold; evolution equation; orbits; Cahn-Hilliard equation},
language = {eng},
number = {3},
pages = {463-488},
publisher = {Dunod},
title = {Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation},
url = {http://eudml.org/doc/193573},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Marion, Martine
TI - Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1989
PB - Dunod
VL - 23
IS - 3
SP - 463
EP - 488
LA - eng
KW - phase transition; approximate inertial manifold; evolution equation; orbits; Cahn-Hilliard equation
UR - http://eudml.org/doc/193573
ER -

References

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  2. [2] J. W. CAHN and J. E. HILLIARD, Free energy of a non uniform system I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258 267. 
  3. [3] P. CONSTANTIN, C. FOIAS, B. NICOLAENKO and R. TEMAM, Integral manifolds and inertial manifolds for dissipative partial differential equations, J. Math. Pures Appl., 67 (1988). Zbl0683.58002MR966192
  4. [4] C. FOIAS, O. MANLEY and R. TEMAM, Sur l'interaction des petits et grands tourbillons dans des écoulements turbulents, C. R. Acad. Sci. Paris, Série I, 305 (1987) 495-500. Zbl0624.76072MR916319
  5. and Modelling of the interaction of small and large eddies in turbulent flows, Math. Mod. and Numer. Anal., 22 (1988) 93-114. Zbl0663.76054
  6. [5] C. FOIAS, G. R. SELL and R. TEMAM, Variétés inertielles des équations différentielles dissipatives, C. R. Acad. Sci. Paris, Série I, 301 (1985) 139-141. Zbl0591.35062MR801946
  7. and Inertial manifolds for nonlinear evolutionary equations, J. Diff. Equ., 73 (1988), 309-353. Zbl0643.58004MR943945
  8. [6] J. S. LANGFR, Theory of spinodal decomposition in alloys, Ann. of Phys., 65 (1971), 53-86. 
  9. [7] J. MALLET-PARET and G. R. SELL, to appear. 
  10. [8] M. MARION, Approximate inertial manifolds for reaction diffusion equations in high space dimension, J. Dynamics and Differential Equations, 1 (1989). Zbl0702.35127MR1010967
  11. [9] M. MARION and R. TEMAM, Nonlinear Galerkin methods, SIAM J. Num. Anal., 26 (1989). Zbl0683.65083MR1014878
  12. [10] B. NICOLAENKO and B. SCHEURER, Low-dimensional behavior of the pattern formation Cahn-Hilliard equation, in Trends in the Theory and Practice of Nonlinear Analysis, V. Lakshmikantham ed., North-Holland, 1985. Zbl0581.35041MR817507
  13. [11] B. NICOLAENKO, B. SCHEURER and R. TEMAM, Some global dynamical properties of a class of pattern formation equations, Comm. Partial Diff. Equ., to appear (see also IMA preprint n° 381, Minneapolis). Zbl0691.35019MR976973
  14. [12] A. NOVICK-COHEN and L. A. SEGEL, Nonlinear aspects of the Cahn-Hilliard equation, Physica D, 10 (1984), 277-298. MR763473
  15. [13] R. TEMAM, Variétés inertielles approximatives pour les équations de Navier-Stokes bidimensionnelles, C. R. Acad. Sci. Paris, Série II, 306 (1988), 399-402. Zbl0638.76035MR979153
  16. [14] R. TEMAM, Infinite dimensional dynamical systems in mechanics and physics, Applied Mathematics Series, vol. 68, Springer-Verlag, New York, 1988. Zbl0662.35001MR953967

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