Blow-up of positive solutions of a semilinear parabolic equation with a gradient term

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 10, Issue 4, 2003, Pages 525-537

  Chlebík, Miroslav ^a   Fila, Marek ^a   Quittner, Pavol ^a  

^a Physics and Informatics   (Slovakia)

Author keywords

Blow up profile; Blow up rate; Blow up set; Nonlinear gradient term; Semilinear parabolic equation

Indexed keywords

EID: 2942549225     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. n for a parabolic equation with a damping nonlinear gradient term, Nonlinear Diffusion Equations and their Equilibrium States, 3 (Gregynog, 1989), pp. 1-20, Progr. Nonlin. Differential Equations Appl., 7, Birkhäuser, Boston, MA, 1992.
2. H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math. 68 (1996), 277-304.
3. M. Chipot and F.B. Weissler, Some blowup results for a nonlinear parabolic equation with a gradient term, SIAM J. Math. Anal. 20 (1989), 886-907.
4. M. Chlebík and M. Fila, From critical exponents to blow-up rates for parabolic problems, Rend. Mat. Appl. 19 (1999), 449-470.
5. M. Fila, Remarks on blow up for a nonlinear parabolic equation with a gradient term, Proc. Amer. Math. Soc. 111 (1991), 795-801.
6. A. Friedman and B. McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447.
7. B. Kawohl and L.A. Peletier, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z., 202 (1989), 207-217.
8. P. Quittner, Blow-up for semilinear parabolic equations with a gradient term, Math. Methods Appl. Sci. 14 (1991), 413-417.
9. P. Quittner, On global existence and stationary solutions of two classes of semilinear parabolic equations, Comment. Math. Univ. Carol. 34 (1993), 105-124.
10. Ph. Souplet, Résultats d'explosion en temps fini pour une équation de la chaleur non linéaire, C. R. Acad. Sc. Paris, Série I 321 (1995), 721-726.
11. Ph. Souplet, Finite time blow up for a nonlinear parabolic equation with a gradient term and applications, Mat. Methods Appl. Sci. 19 (1996), 1317-1333.
12. Ph. Souplet and S. Tayachi, Blow-up rates for nonlinear heat equations with gradient terms and for parabolic inequalities, Colloq. Math. 87 (2001), in press.
13. Ph. Souplet, S. Tayachi and F.B. Weissler, Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term, Indiana Univ. Math. J. 45 (1996), 655-682.
14. Ph. Souplet and F.B. Weissler, Self-similar subsolutions and blow-up for nonlinear parabolic equations, J. Math. Anal. Appl. 212 (1997), 60-74.
15. Ph. Souplet and F.B. Weissler, Poincaré inequality and global solutions of a nonlinear parabolic equation, Ann. Inst. H. Poincaré, Analyse non linéaire 16 (1999), 337-373.