Infinite Time Blow-Up of Solutions to a Nonlinear Parabolic Problem

Journal of Differential Equations

Volumn 139, Issue 2, 1997, Pages 409-427

  Chen, Chao Nien ^a  

^a NATIONAL CHANGHUA UNIVERSITY OF EDUCATION   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039466818     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3289     Document Type: Article

References (38)

1. Angenent S. The zeroset of a solution of a parabolic equation. J. Reine Angew. Math. 1988;1-18.
2. F. V. Atkinson, L. A. Peletier, J. Serrin, Ground states for the prescribed mean curvature equation: the supercritical case, Nonlinear Diffusion Equations and Their Equilibrium States. I, Springer-Verlag, New York.
3. Bebernes J., Bressan A., Eberly D. A description of blow-up for the solid fuel ignition model. Indiana Univ. Math. J. 36:1987;295-305.
4. n. Differential Integral Equations. 7:1994;179-204.
5. Concus P., Finn R. A singular solution of the capillary equation. Invent. Math. 29:1975;143-195.
6. Coffman C. V., Ziemer W. K. Research report. 89-62:1989.
7. Dziuk G., Kawohl B. On rotationally symmetric mean curvature flow. J. Differential Equations. 93:1991;142-149.
8. Ecker K. Estimates for evolutionary surfaces of prescribed mean curvature. Math. Z. 180:1982;179-192.
9. Friedman A. Partial Differential Equations of Parabolic Type. 1983;Krieger.
10. Friedman A., McLeod B. Blow-up of positive solutions of semilinear heat equations. Indiana Univ. Math. J. 34:1985;425-447.
11. Fila M. Boundedness of global solutions of nonlinear diffusion equations. J. Differential Equations. 98:1992;226-240.
12. M. Fila, B. Kawohl, H. A. Levine, Quenching for quasilinear equations.
13. Finn R. Equilibrium Capillary Surfaces. 1986;Springer-Verlag.
14. Gerhardt C. Evolutionary surfaces of prescribed mean curvature. J. Differential Equations. 36:1980;139-172.
15. Giga Y. A bound for global solutions of semilinear heat equations. Comm. Math. Phys. 103:1986;415-421.
16. Giga Y., Kohn R. Nondegeneracy of blow-up for semilinear heat equations. Comm. Pure Appl. Math. 42:1989;845-884.
17. Giusti E. On the equation of surfaces of prescribed mean curvature, Existence and uniqueness without boundary conditions. Invent. Math. 46:1978;111-137.
18. Keller J. B. Plate failure under pressure. SIAM Rev. 22:1980;227-228.
19. Kusano T., Swanson C. A. Radial entire solutions of a class of quasilinear elliptic equations. J. Differential Equations. 83:1990;379-399.
20. Lacey A. A. Gobal blow-up of a nonlinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A. 104:1986;161-167.
21. Ladyženskaja O., Solonnikov V., Uralćeva N. Linear and Quasilinear Equations of Parabolic Type. 1968;Am. Math. Soc. Providence.
22. Levine H. A. The role of critical exponents in blow-up theorems. SIAM Rev. 32:1990;262-288.
23. Levine H. A., Lieberman G. M., Meier P. On critical exponents for some quasilinear parabolic equations. Math. Methods Appl. Sci. 12:1990;429-438.
24. Lichnewsky A., Temam R. Pseudosolutions of the time-dependent minimal surface problem. J. Differential Equations. 30:1978;340-364.
25. Lieberman G. M. Interior gradient bounds for non-uniformly parabolic equation. Indiana Univ. Math. J. 32:1983;579-601.
26. Lin T. P. Maximum area under constraint. Math. Mag. 50:1977;32-34.
27. Marcellini P., Miller K. Asymptotic growth for the parabolic equation of prescribed mean curvature. J. Differential Equations. 51:1984;326-358.
28. Matano H. Convergence of solutions of one-dimensional semilinear parabolic equations. J. Math. Kyota Univ. 18:1978;221-227.
29. Matano H. Nonincrease of the lap number of a solution for a one-dimensional semilinear parabolic equation. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29:1982;401-441.
30. Merle F. Solution of a nonlinear heat equation with arbitrarily given blow-up points. Comm. Pure Appl. Math. 45:1992;263-300.
31. Ni W.-M., Sacks P. E., Tavantzis J. On the asymptotic behavior of solutions of certain quasilinear equations of parabolic type. J. Differential Equations. 54:1984;97-120.
32. Ni W.-M., Serrin J. Existence and non-existence theorems for ground states of quasilinear partial differential equations, the anomalous case. Accad. Naz. Lincei. 77:1986;231-257.
33. Pao C. V. Nonlinear Parabolic and Elliptic Equations. 1992;Plenum.
34. Peletier L. A., Serrin J. Ground states for the prescribed mean curvature equation. Proc. Amer. Math. Soc. 100:1987;694-700.
35. Protter M. H., Weinberger H. F. Maximum Principles in Differential Equations. 1967;Prentice-Hall International, Englewood Cliffs.
36. Serrin J. The problem of Dirichlet for quasi-linear elliptic differential equations with many independent variables. Philos. Trans. Roy. Soc. London Ser. A. 264:1969;413-496.
37. Strang G. A family of model problems in plasticity. Computing Methods in Applied Science and Engineering. Springer-Verlag Lecture Notes in Math. 704:1979;Springer-Verlag.
38. Weissler F. B. Single-point blow-up for a semilinear initial value problem. J. Differential Equations. 55:1984;204-224.