Mosaic solutions and entropy for spatially discrete Cahn-Hilliard equations

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 65, Issue 3, 2000, Pages 219-255

  Abell, K A ^a   Humphries, A R ^a   Van Vleck, E S ^b  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b Department of Metallurgical and Materials Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ENTROPY; INITIAL VALUE PROBLEMS; LYAPUNOV METHODS; MATHEMATICAL MODELS; PHASE TRANSITIONS; PROBLEM SOLVING;

CAHN-HILLIARD EQUATIONS; LATTICE DIFFERENTIAL EQUATIONS; MOSAIC SOLUTIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0034512576     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/65.3.219     Document Type: Article

References (21)

1. ABELL, K. A. 2000 Ph.D. Thesis, University of Sussex, In preparation.
2. BLOWEY, J. F. & ELLIOTT, C. M. 1991 The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy, part I: Mathematical analysis. Eur. J. Appl. Math. 2, 233-280.
3. CAHN, J. W., CHOW, S.-N., & VAN VLECK, E. S. 1995 Spatially discrete nonlinear diffusion equations. Rocky Mountain J. Math. 25, 87-118.
4. CAHN, J. W. & MILLIARD, J. E. 1958 Free energy of a nonuniform system I. Interfacial free energy. J. Chem. Phys. 28, 258-267.
5. CAHN, J. W., MALLET-PARET, J., & VAN VLECK, E. S. 1999 Travelling wave solutions for systems of ODEs on a two-dimensional spatial lattice. SIAM J. Appl. Math. 59, 455-493.
6. CHOW, S.-N., MALLET-PARET, J., & VAN VLECK, E. S. 1996 Dynamics of lattice differential equations. Int. J. Bifurcation and Chaos 6, 1605-1622.
7. CHOW, S.-N., MALLET-PARET, J., & VAN VLECK, E. S. 1996 Pattern formation and spatial chaos in spatially discrete evolution equations. Random and Computational Dynamics 4, 109-178.
8. COOK, H. E., DE FONTAINE, D., & HILLIARD, J. E. 1969 A model for diffusion on cubic lattices and its application to the early stages of ordering. Acta Met. 17, 765-773.
9. COPPEL, W. A. 1965 Stability and Asymptotic Behavior of Differential Equations. Boston: D. C. Heath.
10. ELLIOTT, C. M. 1989 The Cahn-Hilliard model for the kinetics of phase separation. Mathematical Models for Phase Change Problems, Vol. 88, (J. F. Rogrigues ed). Basel: Birkhauser, pp. 97-128.
11. ELLIOTT, C. M. & FRENCH, D. A. 1987 Numerical studies of the Cahn-Hilliard equation for phase separation. IMA J. Appl. Math. 38, 97-128.
12. ELLIOTT, C. M., GARDINER, A. R., KOSTIN, I., & Lu, B. 1994 Mathematical and numerical analysis of a mean-field equation for the Ising model with Glauber dynamics. Contemporary Math. 172, 217-241.
13. HILLERT, M. 1961 A solid-solution model for inhomogeneous systems. Acta Met. 9, 525-535.
14. KLOEDEN, P. E. 1978 General control systems. Mathematical Control Theory, Lecture Notes in Mathematics, 680. (W. A. Coppel ed). Berlin: Springer, pp. 119-137.
15. KREYSZIG, E. 1978 Introductory Functional Analysis with Applications. New York: Wiley.
16. LAPLANTE, J. P. & ERNEUX, T. 1992 Propagation failure in arrays of coupled bistable chemical reactors. J. Phys. Chem. 96, 4931-4934.
17. NOVICK, A. & SEGAL, L. A. 1984 Nonlinear aspects of the Cahn-Hilliard equation. Physica D 10, 277-298.
18. OONO, Y. & PURI, S. 1988 Study of phase-separation dynamics by use of cell dynamical systems. I. modeling. Phys. Rev. A 38, 434-453.
19. PAZY, A. 1983 Semi-groups of Linear Operators and Applications to Partial Differential Equations. Berlin: Springer.
20. ROBINSON, C. 1995 Dynamical Systems. Boca Raton: CRC Press.
21. SENECHAL, M. 1990 Crystalline Symmetries An Informal Mathematical Introduction. Bristol: Hilger.