Immediate regularization after blow-up

SIAM Journal on Mathematical Analysis

Volumn 37, Issue 3, 2006, Pages 752-776

  Fila, Marek ^a   Matano, Hiroshi ^b   Polácik, Peter ^c  

^a Physics and Informatics   (Slovakia)

^b UNIVERSITY OF TOKYO   (Japan)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Blow up; Nonlinear heat equation; Regularity

Indexed keywords

BLOW UP; NONLINEAR HEAT EQUATION; REGULARITY;

FINITE ELEMENT METHOD; MATHEMATICAL MODELS;

NONLINEAR EQUATIONS;

EID: 33646551765     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/040613299     Document Type: Article

References (19)

1. max for the solution of a semilinear heat equation, J. Funct. Anal., 71 (1987), pp. 142-174.
2. X.-Y. CHEN AND P. POLÁČIK, Asymptotic periodicity of positive solutions of reaction-diffusion quations on a ball, J. Reine Angew. Math., 472 (1996), pp. 17-51.
3. M. FILA AND P. POLÁČIK, Global solutions of a semilinear parabolic equation, Adv. Differential Equations, 4 (1999), pp. 163-196.
4. V. GALAKTIONOV AND J.L. VÁZQUEZ, Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math., 50 (1997), pp. 1-67.
5. I.M. GELFAND, Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl., 29 (1963), pp. 295-381.
6. Y. GIGA AND R.V. KOHN, Characterizing blowup using similarity variables, Indiana Univ. Math. J., 36 (1987), pp. 1-40.
7. D.D. JOSEPH AND T.S. LUNDGREN, Quasilinear Dirichlet problems driven by positive sources, Arch. Ration. Mech. Anal., 49 (1973), pp. 241-269.
8. S. KAPLAN, On the growth of solutions of quasi-linear parabolic equations, Commun. Pure Appl. Math., 16 (1963), pp. 305-330.
9. A.A. LACEY AND D.E. TZANETIS, Global, unbounded solutions to a parabolic equation, J. Differential Equations, 101 (1993), pp. 80-102.
10. H. MATANO AND F. MERLE, On non-existence of type II blow-up for a supercritical nonlinear heat equation, Commun. Pure Appl. Math., 57 (2004), pp. 1494-1541.
11. N. MIZOGUCHI, On the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity, Math. Z., 239 (2002), pp. 215-219.
12. N. MIZOGUCHI, Various behaviors of solutions for a semilinear heat equation after blowup, J. Funct. Anal., 220 (2005), pp. 214-227.
13. N. MIZOGUCHI, Multiple blow-up of solutions for a semilinear heat equation, Math. Ann., 331 (2005), pp. 461-473.
14. N. MIZOGUCHI, Multiple Blow-Up of Solutions for a Semilinear Heat Equation II, preprint.
15. N. MIZOGUCHI, Boundedness of Global Solutions for a Semilinear Heat Equation with Supercritical Nonlinearity, preprint.
16. W.-M. NI, P.E. SACKS, AND J. TAVANTZIS, On the asymptotic, behavior of solutions of certain quasilinear parabolic equations, J. Differential Equations, 54 (1984), pp. 97-120.
17. M. PIERRE, private communication.
18. PH. SOUPLET AND F.B. WEISSLER, Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state, Ann. Inst. H. Poincaré, Anal. Non Linéaire, 20 (2003), pp. 213-235.
19. J.L. VÁZQUEZ, Domain of existence and blowup for the exponential reaction diffusion equation, Indiana Univ. Math. J., 48 (1999), pp. 677-709.