Grow-up rate of solutions for a supercritical semilinear diffusion equation

Journal of Differential Equations

Volumn 205, Issue 2, 2004, Pages 365-389

  Fila, Marek ^a   Winkler, Michael ^b   Yanagida, Eiji ^c  

^a Physics and Informatics   (Slovakia)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c TOHOKU UNIVERSITY   (Japan)

Author keywords

Critical exponent; Grow up; Semilinear diffusion equation

Indexed keywords

EID: 4344591249     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.03.009     Document Type: Article

References (14)

1. Dold J.W. Galaktionov V.A. Lacey A.A. Vazquez J.L. Rate of approach to a singular steady state in quasilinear reaction-diffusion equations Ann. Scuola Norm. Sup. Pisa Cl. Sci. 26 1998 663-687
2. 1+α J. Fac. Sci. Univ. Tokyo Sect. I 13 1966 109-124
3. Galaktionov V.A. King J.R. Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents J. Differential Equations 189 2003 199-233
4. Galaktionov V. Vazquez J.L. Continuation of blow-up solutions of nonlinear heat equations in several space dimensions Comm. Pure Appl. Math. 50 1997 1-67
5. n Comm. Pure Appl. Math. 45 1992 1153-1181
6. Gui C. Ni W.-M. Wang X. Further study on a nonlinear heat equation J. Differential Equations 169 2001 588-613
7. Hayakawa K. On nonexistence of global solutions of some semilinear parabolic equations Proc. Japan. Acad. 49 1973 407-424
8. Kavian O. Remarks on the large time behaviour of a nonlinear diffusion equation Ann. Inst. H. Poincaré Anal. Non Linéaire 4 1987 423-452
9. Kobayashi K. Sirao T. Tanaka H. On the growing up problem for semilinear heat equations J. Math. Soc. Japan 29 1977 407-424
10. Matos J. Souplet P. Universal blow-up rates for a semilinear heat equation and applications Adv. Differential Equations 8 2003 615-639
11. Mizoguchi N. On the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity Math. Z. 239 2002 215-229
12. Poláčik P. Yanagida E. On bounded and unbounded global solutions of a supercritical semilinear heat equation Math. Ann. 327 2003 745-771
13. Poláčik P. Yanagida E. Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation Differential and Integral Equations 17 2004 535-548
14. Souplet P. Sur l'asymptotique des solutions globales pour une équation de la chaleur semi-linéaire dans des domaines non bornés C. R. Acad. Sci. Paris Sér. I Math. 323 1996 877-882