Self-similar subsolutions and blowup for nonlinear parabolic equations

Journal of Mathematical Analysis and Applications

Volumn 212, Issue 1, 1997, Pages 60-74

  Souplet, Philippe ^a   Weissler, Fred B ^a  

^a UNIVERSITÉ PARIS 13   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; POROUS MATERIALS; PROBLEM SOLVING;

BLOW UP; BURGERS EQUATION; NONLINEAR PARABOLIC EQUATION; SELF SIMILAR SUBSOLUTION;

NONLINEAR EQUATIONS;

EID: 0031195373     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5452     Document Type: Article

References (28)

1. Aguirre J., Escobedo M. On the blow up of solutions for a convective reaction diffusion equation. Proc. Roy. Soc. Edinburgh. 123A:1993;433-460.
2. Nfor a parabolic equation with a damping nonlinear gradient term. Lloyd N. G. Progress in Nonlinear Differential Equations, Nonlinear Diffusion Equations and Their Equilibrium States, III. 1992;Birkhäuser, Basel.
3. Angenent S., Fila M. Interior gradient blow up in a semilinear parabolic equation. Differential Int. Equations. 9:1996;865-877.
4. Chipot M., Weissler F. B. Some blow up results for a nonlinear parabolic problem with a gradient term. SIAM J. Math. Anal. 20:1989;886-907.
5. Dal Paso R., Luckhaus S. A degenerate diffusion problem not in divergence form. J. Differential Equations. 69:1987;1-14.
6. Fila M. Remarks on blow up for a nonlinear parabolic equation with a gradient term. Proc. Amer. Math. Soc. 111:1991;795-801.
7. Fila M., Lieberman G. Derivative blowup and beyond for quasilinear parabolic equations. Differential Int. Equations. 7:1994;811-821.
8. Fila M., Quittner P. Radial positive solutions for a semilinear elliptic equation with a gradient term. Adv. Math. Sci. Appl. 2:1993;39-45.
9. Friedman A. Partial Differential Equations of Parabolic Type. 1964;Prentice-Hall, Englewood Cliffs.
10. Friedman A. Blow up of solutions of parabolic equations. Ni W. M. Nonlinear Diffusion Equations and Their Equilibrium States, I. 1988;Springer-Verlag, New York/Berlin.
11. Friedman A., Mac Leod B. Blow-up of solutions of nonlinear degenerate parabolic equations. Arch. Rat. Mech. Anal. 96:1986;55-80.
12. β. Differentsial'nye Uravneniya. 17:1981;836-842.
13. Gui C., Wang X. Life span of solutions of the Cauchy problem for a semilinear heat equation. J. Differential Equations. 115:1995;166-172.
14. Kawohl B., Peleitier L. A. Observations on blow up and dead cores for nonlinear parabolic equations. Math. Z. 202:1989;207-217.
15. Ladyzenskaja O. A., Solonnikov V. A., Uralceva N. N. Linear and Quasi-Linear Equations of Parabolic Type. Translations of Mathematical Monographs. 1968;Amer. Math. Soc. Providence.
16. Lee T., Ni W. Global existence, large time behaviour and life span of solutions of a semilinear parabolic Cauchy problem. Trans. Amer. Math. Soc. 333:1992;365-378.
17. Levine H. A., Payne L. N., Sacks P. E., Straughan B. Analysis of convective reaction-diffusion equation (II). SIAM J. Math. Anal. 20:1989;133-147.
18. Levine H. A., Sacks P. E. Some existence and nonexistence theorems for solutions of degenerate parabolic equations. J. Differential Equations. 52:1984;135-161.
19. Quittner P. Blow-up for semilinear parabolic equations with a gradient term. Math. Methods Appl. Sci. 14:1991;413-417.
20. Quittner P. On global existence and stationary solutions for two classes of semilinear parabolic equations. Comment. Math. Univ. Carolinae. 34:1993;105-124.
21. Souplet P. Résultats d'explosion en temps fini pour une équation de la chaleur non linéaire. C. R. Acad. Sci. Paris. 321:1995;721-726.
22. Souplet P. Finite time blow up for a nonlinear parabolic equation with a gradient term and applications. Math. Methods Appl. Sci. 19:1996;1317-1333.
23. Souplet P., Tayachi S., Weissler F. B. Exact self-similar blowup of solutions of a semilinear parabolic equation with a nonlinear gradient term. Indiana Univ. Math. J. 45:1996;655-682.
24. Voirol F. Coexistence of singular and regular solutions for the equation of Chipot and Weissler. Acta Math. Univ. Comenianae. 65:1996;53-64.
25. Weissler F. B. Semilinear evolution equations in Banach Spaces. J. Funct. Anal. 32:1979;277-296.
26. p. Indiana Univ. Math. J. 29:1980;79-102.
27. Wiegner M. Blow-up for solutions of some degenerate parabolic equations. Differential Int. Equations. 7:1994;1641-1647.
28. M. Wiegner, A degenerate diffusion equation with a nonlinear source term.