Regularity of solutions of the Cahn-Hilliard equation with non-constant mobility

Acta Mathematica Sinica, English Series

Volumn 22, Issue 4, 2006, Pages 1139-1150

  Liu, Chang Chun ^a   Qi, Yuan Wei ^b   Yin, Jing Xue ^a  

^a JILIN UNIVERSITY   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cahn Hilliard equation; Regularity; Schauder estimates

Indexed keywords

EID: 33746409633     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-005-0711-5     Document Type: Article

References (23)

1. Novick-Cohen, A., Segel, L. A.: Nonlinear aspects of the Cahn - Hilliard equation. Physica D, 10, 277-298 (1984)
2. Cohen, D. S., Murrey, J. D.: A generalized diffusion model for growth and dispersal in a population. J. Math. Biology, 12, 237-249 (1981)
3. Pego, R. L.: Front migration in the nonlinear Cahn - Hilliard equation. Proc. R. Soc. Lond., A, 422, 261-278 (1989)
4. Taylor, A. B.: Mathematical Models in Applied Mechanics, Clarendon, Oxford, 1986
5. Zheng, S. M.: Mathematical results on the coupled Cahn - Milliard equations, Proceedings of the Conference on Nonlinear Evolution Equations and Infinite-dimensional Dynamical Systems (Shanghai, 1995), 259-265, World Sci. Publishing, River Edge, NJ, 1997
6. Elliott, C. M., Zheng, S. M.: On the Cahn - Hilliard equation. Arch. Rat. Mech. Anal., 96, 339-357 (1986)
7. Novick-Cohen, A.: On Cahn - Hilliard type equations. Nonlinear Analysis. TMA, 15, 797-814 (1990)
8. Chen, X.: Global asymptotic limit of solutions of the Cahn - Hilliard equation. J. Differential Geom., 44, 262-311 (1996)
9. Alikakos, N. D., Bates, P. W., Chen, X. F.: Asymptotics of the Cahn - Hilliard flow, Curvature flows and related topics (Levico, 1994), 13-23, GAKUTO Internat. Ser. Math. Sci. Appl., 1, Gakkōtosho, Tokyo, 1995
10. Bernis, F., Friedman, A.: Higher order nonlinear degenerate parabolic equations. Journal of Differential Equations, 83, 179-206 (1990)
11. Yin, J.: On the existence of nonnegative continuous solutions of the Cahn - Hilliard equation. Journal of Differential Equations, 97, 310-327 (1992)
12. Yin, J.: On the Cahn - Hilliard equation with nonlinear principal part. Journal of Partial Differential Equations, 7, 77-96 (1994)
13. Bernis, F.: Finite speed of propagation and continuity of the interface for thin viscous flows. Adv. Differential Equations, 1, 337-368 (1996)
14. Bernis, F.: Qualitative properties for some nonlinear higher order degenerate parabolic equations. Houston J. of Math., 14, 319-351 (1988)
15. Elliott, C. M., Garcke, H.: On the Cahn - Hilliard equation with degenerate mobility. SIAM, J. Math. Anal., 27, 404-423 (1996)
16. Garcke, H., Novick-Cohen, A.: A singular limit for a system of degenerate Cahn - Hilliard equations. Adv. Differential Equations, 5, 401-434 (2000)
17. Barrett, J. W., Blowey, J. F., Garcke, H.: Finite element approximation of the Cahn - Hilliard equation with degenerate mobility. SIAM J. Numer. Anal., 37, 286-318 (1999)
18. Barrett, J. W., Blowey, J. F.: Finite element approximation of the Cahn - Hilliard equation with concentration dependent mobility. Math. Comp., 68, 487-517 (1999)
19. Witelski, T. P.: Equilibrium interface solutions of a degenerate singular Cahn - Hilliard equation. Appl. Math. Lett., 11, 127-133 (1998)
20. Yin, J., Liu, C.: Regularity of solutions of the Cahn - Hilliard equation with concentration dependent mobility. Nonlinear Analysis, TMA., 45, 543-554 (2001)
21. Giaquinta, M., Strume, M.: On the partial regularity for weak solutions to nonlinear parabolic systems. Math. Z., 179, 437-451 (1982)
22. Zhang, W.: Maximal attractors for the m-Dimensional Cahn - Hilliard system. Acta Mathematica Sinica, English Series, 20(2), 233-246 (2004)
23. Zhang, W.: Dimension of maximal attractors for the m-dimensional Cahn - Hilliard System. Acta Mathematica Sinica, English Series, 21(6), 1487-1494 (2005)