Propagation of fronts in a nonlinear fourth order equation

European Journal of Applied Mathematics

Volumn 11, Issue 2, 2000, Pages 203-213

  Loreti, P ^a,b   March, R ^b  

^a CNR   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034420272     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792599004131     Document Type: Article

References (25)

1. ALIKAKOS, N. D., BATES, P. W. & CHEN, X. (1994) Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Arch. Rational Mech. Anal. 128, 165-205.
2. ALLEN, S. M. & CAHN J. W. (1979) A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Met. 27, 1085-1095.
3. BELLETTINI, G., DAL MASO, G. & PAOLINI, M. (1993) Semicontinuity and relaxation properties of a curvature depending functional in 2D. Annali Scuola Normale Superiore Pisa 20, 247-299.
4. BELLETTINI, G. & PAOLINI, M. (1993) Approssimazione variazionale di funzionali con curvatura. Seminario di Analisi Matematica, Dipartimento di Matematica dell' Universitá di Bologna.
5. CAGINALP, G. & FIFE, P. C. (1988) Dynamics of layered interfaces arising from phase boundaries. SIAM J. Appl. Math. 48, 506-518.
6. CAGINALP, G. (1989) Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. Phys. Rev. A 39, 5887-5896.
7. CAGINALP, G. (1990) The dynamics of a conserved phase-field system: Stefan-like, Hele-Shaw, and Cahn-Hilliard models as asymptotics limits. IMA J. Appl. Math. 44, 77-94.
8. CAHN, J. W. (1961) On spinoidal decomposition. Acta Met. 9, 795-801.
9. CAHN, J. W., ELLIOTT, C. M. & NOVICK-COHEN, A. (1996) The Cahn-Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature. Euro. J. Appl. Math. 7, 287-301.
10. CAHN, J. W. & TAYLOR, J. E. (1994) Surface motion by surface diffusion. Acta metall. mater. 42, 1045-1063.
11. COHEN, L. D. (1991) On active contour models and balloons. CVGIP: Image Understanding 53, 211-218.
12. COHEN, I., COHEN, L. D. & AYACHE, N. (1992) Using deformable surfaces to segment 3-D images and infer differential structures. CVGIP: Image Understanding 56, 242-263.
13. DE GIORGI, E. (1991) Some remarks on Γ-convergence and least squares methods. In: Composite Media and Homogeneization Theory (G. Dal Maso and G. F. Dell'Antonio, eds.), Progress in Nonlinear Differential Equations and their Applications, Vol. 5, Birkhauser.
14. DI CARLO, A., GURTIN, M. E. & PODIO-GUIDUGLI, P. (1992) A regularized equation for anisotropic motion-by-curvature. SIAM J. Appl. Math. 52, 1111-1119.
15. EVANS, L. C., SONER, H. M. & SOUGANIDIS, P. E. (1992) Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math. 45, 1097-1123.
16. ILMANEN, T. (1993) Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature. J. Diff. Geom. 38, 417-461.
17. KASS, M., WITKIN, A. & TERZOPOULOS, D. (1987) Snakes: active contour models. Int. J. Comput. Vision 1, 321-331.
18. KICHENASSAMY, S., KUMAR, A., OLVER, P., TANNENBAUM, A. & YEZZI JR., A. (1996) Conformal curvature flows: from phase transitions to active vision. Arch. Rational Mech. Anal. 134, 275-301.
19. LEYMARIE, F. & LEVINE, M. D. (1993) Tracking deformable objects in the plane using an active contour model. IEEE Trans. PAMI 15, 617-634.
20. MARCH, R. & DOZIO, M. (1997) A variational method for the recovery of smooth boundaries. Image and Vision Computing 15, 705-712.
21. MOREL, J. M. & SOLIMINI, S. (1995) Variational Methods in Image Segmentation, Progress in Nonlinear Differential Equations and their Applications, 14. Boston. Birkhauser.
22. NITZBERG, M., MUMFORD, D. & SHIOTA, T. (1993) Filtering, Segmentation and Depth. Springer-Verlag.
23. NOCHETTO, R. H., PAOLINI, M. & VERDI, C. (1996) A dynamic mesh algorithm for curvature dependent evolving interfaces. J. Comput. Physics 123, 296-310.
24. PEGO, R. L. (1989) Front migration in the nonlinear Cahn-Hilliard equation. Proc. R. Soc. Lond. A 422, 261-278.
25. RUBINSTEIN, J., STERNBERG, P. & KELLER, J. B. (1989) Fast reaction, slow diffusion, and curve shortening. SIAM J. Appl. Math. 49, 116-133.