| Title:
|
A blow-up result for nonlinear diffusion equations (English) |
| Author:
|
Fila, Marek |
| Author:
|
Filo, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1989 |
| Pages:
|
331-346 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B40 |
| MSC:
|
35K57 |
| idZBL:
|
Zbl 0704.35071 |
| idMR:
|
MR1016350 |
| . |
| Date available:
|
2009-09-25T10:19:26Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132074 |
| . |
| Reference:
|
[1] ARONSON D. G., CRANDALL M. G., PELETIER L. A.: Stabilization of solutions of a degenerate nonlinear diffusion problem.Nonlinear Analysis, 6, 1982, 1001-1022. Zbl 0518.35050, MR 0678053 |
| Reference:
|
[2] BALL J. M.: Remarks on blow-up and nonexistence theorems for nonlinear evolution equations.Quart. J. Math. Oxford, (2), 28, 1977, 473-486. Zbl 0377.35037, MR 0473484 |
| Reference:
|
[3] BERGER M. S.: Nonlinearity and functional analysis.Academic Press 1977. Zbl 0368.47001, MR 0488101 |
| Reference:
|
[4] FILA M., FILO J.: Stabilization of solutions of certain one-dimensional degentrate diffusion equations.Math. Slovaca 37, 1987, 217-229. MR 0899439 |
| Reference:
|
[5] FILO J.: On solutions of a pertuгbed fast diffusion equation.Aplikace matematiky 32, 1987, 364-380. MR 0909544 |
| Reference:
|
[6] FRIEDMAN A.: Partial differential equations of parabolic type.Prentice-Hall, N.J. 1964. Zbl 0144.34903, MR 0181836 |
| Reference:
|
[7] FRIEDMAN A.: Partial differential equations.Holt, Rinehart and Winston, New York 1969. Zbl 0224.35002, MR 0445088 |
| Reference:
|
[8] FUJITA H.: On the blowing up of solutions of the Cauchy problem for $u_t = \bigtriangleup u + u^{1+a}.$.J. Fac. Sci. Univ. Tokyo, Sect. 1A 13, 1966, 109-124. MR 0214914 |
| Reference:
|
[9] GALAKTIONOV V. A.: A boundary value problem for the nonlinear parabolic equation $u_t = ∆u^{1+\alpha} + u^\beta$.Differential equations 17, 1981, 551-555 (Russian). MR 0616920 |
| Reference:
|
[10] LADYZENSKAJA O. A., SOLONNIKOV V. A., URALCEVA N. N.: Lineaг and quasilinear equations of paгabolic type.Nauka, Moscow 1967. |
| Reference:
|
[11] LEVINE H. A., SACKS P. E.: Some existence and nonexistence theorems for solutions of degenerate parabolic equations.J. Differential Equations 52, 1984, 135-161. Zbl 0487.34003, MR 0741265 |
| Reference:
|
[12] NAKAO M.: Existence, nonexistence and some asymptotic behaviour of global solutions of a nonlinear degenerate parabolic equation.Math. Rep. College of Gen. Edc, Kyushu Univ. 14, 1983, 1-21. Zbl 0563.35038, MR 0737351 |
| Reference:
|
[13] NAKAO M.: Lp-estimates of solution of some nonlinear degenerate diffusion equations.J. Math. Soc. Japan 37, 1985, 41-63. MR 0769776 |
| Reference:
|
[14] SACKS P. E.: Continuity of solutions of a singular parabolic equation.Nonlinear Analysis 7, 1983, 387-409. Zbl 0511.35052, MR 0696738 |
| Reference:
|
[15] SATTINGER D. H., PAYNE L. E.: Saddle points and instability of nonlinear hyperbolic equations.Israel J. Math. 22, 1975, 273-303. MR 0402291 |
| Reference:
|
[16] TSUTSUMI M.: Existence and nonexistence of global solutions for nonlinear parabolic equations.Publ. R.I.M.S., Kyoto Univ. 8, 1972/73, 211-229. Zbl 0248.35074, MR 0312079 |
| . |
