A Cahn-Hilliard model in bounded domains with permeable walls

Mathematical Methods in the Applied Sciences

Volumn 29, Issue 17, 2006, Pages 2009-2036

  Gal, Ciprian G ^a  

^a University of Memphis   (United States)

Author keywords

Cahn Hilliard equation; Dynamic boundary conditions; Wentzell boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; PHASE SEPARATION; POROUS MATERIALS; PROBLEM SOLVING; WALLS (STRUCTURAL PARTITIONS);

CAHN-HILLIARD EQUATION; DYNAMIC BOUNDARY CONDITIONS; WENTZELL BOUNDARY CONDITIONS;

BINARY MIXTURES;

EID: 33750804502     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.757     Document Type: Article

References (28)

1. Cahn JW, Hilliard E. Free energy of a nonuniform system. Journal of Chemical Physics 1958; 28:258-367.
2. Novack-Cohen A. The Cahn-Hilliard equation: mathematical and modeling perspectives. Advances in Mathematical Sciences and Applications 1998; 8:965-985.
3. Kenzler R, Eurich F, Maass P, Rinn B, Schropp J, Bohl E, Dieterich W. Phase separation in confined geometries: solving the Cahn-Hilliard equation with generic boundary conditions. Computer Physics Communications 2001; 133:139-157.
4. Elliott CM, Zheng S. On the Cahn-Hilliard equation. Archive for Rational Mechanics and Analysis 1986; 96:339-357.
5. Zheng S. Asymptotic behavior of solutions to the Cahn-Hilliard equations. Applied Analysis 1986; 3:165-184.
6. Zheng S. Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems. Pitman Monographs Surv. Pure Appl. Math., vol. 76. Longman/Wiley: New York, 1995.
7. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematics and Sciences, vol. 68. Springer: New York, 1988.
8. Kenmochi N, Niezgodka M, Pawlow I. Subdifferential operator approach to the Cahn-Hilliard equations with constraint. Journal of Differential Equations 1995; 117:320-356.
9. Racke R, Zheng S. The Cahn-Hilliard equation with dynamical boundary conditions. Advances in Differential Equations 2003; 8:83-110.
10. Pruss J, Racke R, Zheng S. Maximal regularity and asymptotic behavior of solutions for the Cahn-Hilliard equation with dynamic boundary conditions. Annali di Matematica Pura ed Applicata 2005; electronic: 1618-1891.
11. Miranville A, Zelik S. Robust exponential attractors for Cahn-Hilliard type equations with singular potential. Mathematical Models and Methods in Applied Science 2004; 27:545-582.
12. Wu H, Zheng S. Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions. Journal of Differential Equations 2004; 204:511-531.
13. Chill R, Fasangova E, Pruss J. Convergence to steady states of solutions of the Cahn-Hilliard and Caginalp equations with dynamic boundary conditions. Mathematische Nachrichten 2006, in press.
14. Elliott CM, Zheng S. Global Existence and Stability of Solutions to the Phase-Field Equations, Free Boundary Problems. International Series of Numerical Mathematics, vol. 95. Birkhauser: Basel, 1990; 46-58.
15. Cohen DS, Murray JD. A generalized diffusion model for growth and dispersal in a population. Journal of Mathematical Biology 1981; 12:237-249.
16. Goldstein GR. Derivation and physical interpretation of general boundary conditions. Advances in Differential Equations 2006; 11(4):457-480.
17. p spaces. Proceedings of the Equadiff 10, Prague, 27-31 August 2001.
18. Favini A, Goldstein GR, Goldstein JA, Romanelli S. The heat equation with general Wentzell boundary conditions. Journal of Evolution Equations 2002; 2:1-19.
19. Caginalp G. An analysis of a phase field model of a free boundary. Archive for Rational Mechanics and Analysis 1986; 92:205-245.
20. Amann H. Parabolic evolution equations and nonlinear boundary conditions. Journal of Differential Equations 1988; 72:201-269.
21. Amann H, Escher J. Strongly continuous dual semigroups. Annali di Matematica Pura ed Applicata 1996; CLXXI(IV):41-62.
22. Grobbelaar-Van Dalsen M, Sauer N. Dynamic boundary conditions for Navier-Stokes equations. Proceedings of the Royal Society of Edinburg, Section A 1989; 113:1-11.
23. Hintermann T. Evolution equations with dynamic boundary conditions. Proceedings of the Royal Society of Edinburg, Section A 1989; 113:43-60.
24. Warma M. Wentzell-Robin boundary conditions on C[0, 1]. Semigroup Forum 2003; 66:162-170.
25. Engel KJ, Fragnelli G. Analiticity of semigroups generated by operators with generalized Wentzell boundary conditions. Advances in Differential Equations 2005; 10(11):1301-1320.
26. Hörmander L. Linear Partial Differential Operators. Grundlehren Math. Wiss., vol. 116. Springer: Berlin, 1976.
27. Peetre J. Another approach to elliptic boundary value problems. Communications on Pure and Applied Mathematics 1961; 14:711-731.
28. Višik MI. On general boundary problems for elliptic differential equations. Trudy Moskovskoga Matematicheskogo Obshehestra 1952; 1:187-246 (in Russian).