Stability of stationary interfaces with contact angle in a generalized mean curvature flow

American Journal of Mathematics

Volumn 118, Issue 3, 1996, Pages 653-687

  Ei, S I ^a   Sato, M H ^b   Yanagida, E ^c  

^a YOKOHAMA CITY UNIVERSITY   (Japan)

^b MURORAN INSTITUTE OF TECHNOLOGY   (Japan)

^c TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040056192     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. G. Barles, H. M. Soner, and P. E. Souganidis, Front propagation and phase field theory, SIAM J. Control Optim. 31 (1993), 439-469.
2. X. Chen, Generation and propagation of interfaces for reaction-diffusion equations, J. Differential Equations 96 (1992), 116-141.
3. Y.-G. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33 (1991), 749-786.
4. M. G. Crandall, H. Ishii, and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), 1-67.
5. P. De Mottoni and M. Shatzman, Geometrical evolution of developed interfaces, Equipe d'Analyse Numèrique Lyon Saint-Etienne CNRS URA 740, No. 87, 1989.
6. S.-I. Ei, M. Iida, and E. Yanagida, Dynamics of interfaces in a scalar parabolic equation with variable diffusion, Japan J. Indust. Appl. Math. (to appear).
7. S.-I. Ei and E. Yanagida, Stability of stationary interfaces in a generalized mean curvature flow, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40 (1994), 651-661.
8. _, Instability of stationary solutions for equations of curvature-driven motion of curves, J. Dynamics Differential Equations 7 (1995), 423-435.
9. L. C. Evans, H. M. Soner, and P. E. Souganidis, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. XLV (1992), 1097-1123.
10. L. C. Evans and J. Spruck, Motion of level sets by mean curvature I, J. Differential Geom. 33 (1991) 635-681.
11. _, Motion of level sets by mean curvature II, Trans. Amer. Math. Soc. 330 (1992), 321-332.
12. _, Motion of level sets by mean curvature III, J. Geom. Anal. 2 (1992), 121-150.
13. _, Motion of level sets by mean curvature IV, preprint.
14. P. C. Fife, Dynamics of Internal Layers and Diffusive Interfaces, CCMS-NSF Regional Conf. Ser. in Appl. Math., SIAM, Philadelphia, 1988.
15. M. Gage and R. Hamilton, The shrinking of convex plane curves to points, J. Differential Geom. 23 (1986), 69-96.
16. Y. Giga, S. Goto, H. Ishii, and M.-H. Sato, Comparison principle and convexity preserving properties for singular degenerate parabolic equations in unbounded domain, Indiana Univ. Math. J. 77 (1991), 443-470.
17. Y. Giga and K. Yamauchi, On instability of evolving hypersurfaces, Differential Integral Equations 7 (1994), 863-872.
18. M. Grayson, The heat equation shrinks embedded plane curves to points, J. Differential Geom. 26 (1987), 285-314.
19. G. Huisken, Flow by mean curvature of convex surface into surface, J. Differential Geom. 20 (1984), 237-266.
20. M. Katsoulakis, G. T. Kossioris, and F. Reitich, Generalized motion by mean curvature with Neumann conditions and the Allen-Cahn model for phase transitions, J. Geom. Anal. (to appear).
21. R. Kobayashi, Modeling and numerical simulations of dendritic crystal growth, Phys. D 63 (1993), 410-423.
22. K. Kawasaki and T. Ohta, Kinetic drumhead model of interface I, Progr. Theoret. Phys. 67 (1982), 147-163.
23. N. C. Owen and P. Sternberg, Gradient flow and front propagation with boundary contact energy, Proc. Roy. Soc. London Ser. A 437 (1992), 715-728.
24. J. Rubinstein, P. Sternberg, and J. B. Keller, Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math. 49 (1989), 116-133.
25. M.-H. Sato, Interface evolution with Neumann boundary condition, Adv. Math. Sci. Appl. 4 (1994), 249-264.
26. _, Capillary problem for singular degenerate parabolic equation on a half space, Differential Integral Equations (to appear).
27. M.-H. Sato and H. Ishii, Capillary problem for singular degenerate parabolic equations on a general domain, in preparation.