A fujita type result for a degenerate Neumann problem in domains with noncompact boundary

Journal of Mathematical Analysis and Applications

Volumn 231, Issue 2, 1999, Pages 543-567

  Andreucci, Daniele ^a   Tedeev, Anatoli F ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007293409     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6253     Document Type: Article

References (19)

1. Andreucci D. Degenerate parabolic equations with initial data measures. Transactions Amer. Math. Soc. 349:1997;3911-3923.
2. Andreucci D., DiBenedetto E. On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18:1991;363-441.
3. D. Andreucci, A. F. Tedeev, Sharp estimates and finite speed of propagation for a Neumann problem in domains narrowing at infinity.
4. Bénilan P., Wittbold P. On mild and weak solutions of elliptic-parabolic problems. Adv. Differential Equations. 1:1996;1053-1073.
5. Bernis F. Qualitative properties for some nonlinear higher order degenerate parabolic equations. Houston J. Math. 14:1988;319-352.
6. DiBenedetto E. Degenerate Parabolic Equations. 1993;Springer, New York.
7. Galaktionov V. A. Blow-up for quasilinear heat equations with critical Fujita's exponent. Proc. Roy. Soc. Edinburgh Sect. A. 124:1994;517-525.
8. Gushchin A. K. The rate of stabilization of a solution of a parabolic equation in an unbounded region. Differentsial'nye Uravnenyi. 6:1970;741-761.
9. Gushchin A. K. On estimates of solutions of boundary value problems for for a second order parabolic equation. Trudy Mat. Inst. Steklov. 126:1973;5-45.
10. Gushchin A. K. On the uniform stabilization of solutions of the second mixed problem for a parabolic equation. Mat. Sb. 119:1982.
11. Ivanov A. V. Holder estimates near the boundary for generalized solutions of quasilinear parabolic equations that admit double degeneration. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 188:1991;45-69.
12. Ladyzhenskaja O. A., Solonnikov V. A., Ural'ceva N. N. Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs. 23:1968;American Mathematical Society, Providence.
13. Levine H. A. The role of critical exponents in blowup theorems. SIAM Review. 32:1990;262-288.
14. Lieberman G. M. The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations. Commun. Partial Differential Equations. 16:1991;311-361.
15. Maz'ja V. G. Sobolev Spaces. Springer Series in Soviet Mathematics. 1985;Springer, Berlin.
16. Porzio M., Vespri V. Holder estimates for local solutions of some doubly nonlinear degenerate parabolic equations. J. Differential Equations. 103:1993;146-178.
17. Tedeev A. F. Qualitative properties of solutions of Neumann problem for quasilinear higher order parabolic equations. Ukrainian Math. J. 44:1993;1571-1579.
18. Tedeev A. F. Two sided estimates ast. Ukrainian Math. J. 48:1996;989-998.
19. Tsutsumi M. On solutions of some doubly nonlinear parabolic equations with absorption. J. Math. Anal. Appl. 132:1988;187-212.