The critical exponents of parabolic equations and blow-up in Rn

Royal Society of Edinburgh - Proceedings A

Volumn 128, Issue 1, 1998, Pages 123-136

  Qi, Yuan Wei ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

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EID: 21944448306     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500027190     Document Type: Article

References (26)

1. J. Aguirre and M. Escobedo. On the blow-up of solutions of a convective reaction diffusion equation. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 433-60.
2. D. G. Aronson and H. F. Weinberger. Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 30 (1978), 33-76.
3. C. Bandle and H. Levine. On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains. Trans. Amer. Math. Soc. 655 (1989), 595-624.
4. Y. Z. Chen. Hölder continuity of the gradients of solutions of nonlinear degenerate parabolic systems. Acta Math. Sinica, NS 2 (1986), 309-31.
5. Y. Z. Chen and E. Di Benedetto. On the local behaviour of solutions of singular parabolic equations. Arch. Rational Mech. Anal. 103 (1988), 319-45.
6. Y. Z. Chen and E. Di Benedetto. Boundary estimates for solutions of nonlinear degenerate parabolic systems. J. Reine Angew. Math. 395 (1989), 102-31.
7. 1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983), 827-50.
8. M. Escobedo and M. A. Herrero. Boundedness and blow up for a semilinear reaction-diffusion system. J. Differential Equations 89 (1991), 176-202.
9. A. Friedman and J. B. McLeod. Blow-up of positive solutions of semilinear heat equations. Indiana Univ. Math. J. 34 (1985), 425-77.
10. 1+α. J. Fac. Sci. Tokyo Sect. IA, Math. 13 (1966), 102-24.
11. V. A. Galaktionov. Blow-up for quasilinear heat equations with critical Fujita's exponents. Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), 517-25.
12. β. Soviet Phys. Dokl. 25 (1980), 458-9.
13. A. Haraux and F. B. Weissler. Nonuniqueness for a semilinear initial problem. Indiana Univ. Math. J. 31 (1982), 167-89.
14. K. Hayakawa. On nonexistence of global solutions of some semilinear parabolic equations. Proc. Japan Acad. 49 (1973), 503-25.
15. m when 0 < m < 1. Trans. Amer. Math. Soc. 291 (1985), 145-58.
16. K. Kobayashi, T. Sirao and H. Tanaka. On the blowing up problems for semilinear heat equation. J. Math. Soc. Japan 29 (1977), 407-24.
17. H. A. Levine. A Fujita type global existence-global non-existence theorem for a weakly coupled system of reaction-diffusion equations. ZAMP 42 (1990), 408-30.
18. H. A. Levine, G. Lieberman and P. Meier. On critical exponent for some quasilinear parabolic equations. Math. Meth. Appl. Sci. 109 (1992), 73-80.
19. H. A. Levine and P. Meier. A blowup result for the critical exponent in cones. Israel J. Math. 67 (1989), 1-8.
20. H. A. Levine and P. Meier. The value of the critical exponent for reaction-diffusion equations in cones. Arch. Rational Mech. Anal. 109 (1989), 73-80.
21. K. Mochizuki and K. Mukai. Existence and nonexistence of global solutions to fast diffusions with source. Math. Appl. Anal. 2 (1994), 92-102.
22. β. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 373-90.
23. Y. W. Qi. The existence of moving boundary solution of a porous media equation with a source term. Adv. Math. Sci. Appl. (1994) (to appear).
24. Y. W. Qi. The critical exponents of degenerate parabolic equations. Sci. China Ser. A 38 (1994), 1153-62.
25. Y. W. Qi and H. Levine. The critical exponent of degenerate parabolic systems. ZAMP 44 (1993), 249-65.
26. F. B. Weissler. Existence and nonexistence of global solutions for semilinear heat equations. Israel J. Math. 38 (1981), 29-40.