On instant extinction for very fast diffusion equations

Discrete and Continuous Dynamical Systems

Volumn 3, Issue 2, 1997, Pages 243-250

  Chen, Yun Gang ^a   Giga, Yoshikazu ^b   Sato, Koh ^c  

^a TOKAI UNIVERSITY   (Japan)

^b HOKKAIDO UNIVERSITY   (Japan)

^c OTARU UNIVERSITY OF COMMERCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031526062     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1997.3.243     Document Type: Article

References (16)

1. S. Angenent and M. Gurtin, Multiphase thermomechanics with interfacial structure 2, Evolution of an isothermal interface, Arch. Rational Mech. Anal., 108(1989), 323-391.
2. Y.-G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Diff. Geometry, 33(1991), 749-786.
3. E. DiBenedetto, Degenerate Parabolic Equations, Springer-Verlag, 1993.
4. L. C. Evans, A geometric interpretation of the heat equations with multivalued initial data , SIAM J. Math. Anal., 27(1996), 932-958.
5. L. C. Evans and J. S. Spruck, Motion of level sets by mean curvature I, J. Diff. Geometry, 23(1991), 635-681.
6. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, Inc, New York, 1969.
7. M.-H. Giga and Y. Giga, Consistency in evolutions by crystalline curvature , Proc. Free Boundary Problems '95, Theory and Applications, (ed. M. Niezgódka), Zakopane, Poland (1995), to appear.
8. M.-H. Giga and Y. Giga, Geometric evolution by nonsmooth interfacial energy , Proceedings of Banach Center Minisemester, Nonlinear Analysis and Applications (eds. N. Kenmochi, M. Niezgódka and P. Strzelecki), Gakuto, Tokyo (1995), pp.125-140.
9. M.-H. Giga and Y. Giga, Evolving graphs by singular weighted curvature , Arch. Rational Mech. Anal., to appear.
10. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, Berlin, 1983.
11. S. Goto, Generalized motion of hypersurfaces whose growth speed depends superlinearly on the curvature tensor, Diff. Int. Equations, 7(1994), 323-343.
12. H. Ishii and P. E. Souganidis, Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor, Tôhoku Math. J., 47(1995), 227-250.
13. O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1967.
14. M. Ohnuma and K. Sato, Singular degenerate parabolic equations with applications to the p-Laplace diffusion equation, preprint.
15. J. Taylor, Constructions and conjectures in crystalline nondifferential geometry , Pitman Monographs in Pure and Applied Mathematics (eds. B. Lawson and K. Tanenblat), 52 (1991), 321-336.
16. J. L. Vazquez, Nonexistence of solutions for nonlinear heat equations of fast-diffusion type, J. Math. Pures Appl., 71(1992), 503-526.