Ginzburg-Landau equation and motion by mean curvature, II: Development of the initial interface

Journal of Geometric Analysis

Volumn 7, Issue 3, 1997, Pages 477-491

  Soner, Halil Mete ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Ginzburg Landau equation; Maximum principle; Traveling waves

Indexed keywords

EID: 0037695861     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02921629     Document Type: Article

References (13)

1. Barles, G., Soner, H. M., and Souganidis, P. E. Front propagation and phase field theory. SIAM. J. Cont. Opt. 31, 439-469 (1993).
2. Chen, X. Generation and propagation of the interface for reaction-diffusion equations. J. Differential Eq. 96, 116-141 (1992).
3. Evans, L. C., and Gariepy, R. F. Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton, 1992.
4. Evans, L. C., Soner, H. M., and Souganidis, P. E. Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math. 45, 1097-1123 (1992).
5. Fife, P. C., and McLeod, B. The approach of solutions of nonlinear diffusion equation to travelling front solutions. Arc. Ratl. Mech. An. 65, 335-361 (1977).
6. Guisti, E. Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston, 1984.
7. Ilmanen, T. Convergence of the Allen-Cahn equation to the Brakke's motion by mean curvature. Preprint (1991).
8. deMottoni, P., and Schatzman, M. Geometrical evolution of developed interfaces. Trans. AMS to appear.
9. (Announcement: Evolution géométric d'interfaces. C.R. Acad. Sci. Sér. 1. Math. 309, 453-458 (1989).)
10. d. Proc. Royal Edinburgh Sect. A 116, 207-220 (1990).
11. Rubinstein, J., Sternberg, P., and Keller, J. B. Fast reaction, slow diffusion and curve shortening. SIAM J. Appl. Math. 49, 116-133 (1989).
12. Soner, H. M. Motion of a set by the curvature of its boundary. J. Differential Equations 101/2, 313-372 (1993).
13. Soner, H. M. Ginzburg-Landau equation and motion by mean curvature, I: Convergence. Preprint.