| Title:
|
Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions (English) |
| Author:
|
Filo, Ján |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1989 |
| Pages:
|
485-495 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35K05 |
| MSC:
|
35K55 |
| MSC:
|
35K60 |
| idZBL:
|
Zbl 0702.35142 |
| idMR:
|
MR1031866 |
| . |
| Date available:
|
2008-06-05T21:39:43Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106770 |
| . |
| Reference:
|
[1] Alikakos N. D.: $L^p$ bounds of solutions of reaction-diffusion equations.Comm. Partial Differential Equations 4 (1979), 827-868. MR 0537465 |
| Reference:
|
[2] Amann H.: Quasilinear parabolic systems under nonlinear boundary conditions.Arch. Rat. Mech. Anal. 92 (1986), 153-192. Zbl 0596.35061, MR 0816618 |
| Reference:
|
[3] DiBenedetto E.: Continuity of weak solutions to a general porous medium equation.Indiana Univ. Math. J. 32 (1983), 83-118. Zbl 0526.35042, MR 0684758 |
| Reference:
|
[4] Fila M.: Boundedness of global solutions for the heat equation with nonlinear boundary conditions.Comment. Math. Univ. Carolinae 30 (1989), 479-484. Zbl 0702.35141, MR 1031865 |
| Reference:
|
[5] Filo J.: $L^∞$-estimate for nonlinear diffusion equations.manuscript. Zbl 0849.35061 |
| Reference:
|
[6] Friedman A., McLeod B.: Blow-up of positive aolutiona of aemilinear heat equations.Indiana Univ. Math. J. 34 (1985), 425-447. MR 0783924 |
| Reference:
|
[7] Ladyzhenskaya O. A., Solonikov V. A., Uraltseva N. N.: Linear and Quasi-linear Equations of Parabolic Type.Nauka, Moscow, 1967. |
| Reference:
|
[8] Levine H. A., Payne L. E.: Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time.J. Diff. Eqns. 16 (1974), 319-334. MR 0470481 |
| Reference:
|
[9] Nakao M.: Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations.Nonlinear Analysis 10 (1986), 299-314. Zbl 0595.35058, MR 0834507 |
| Reference:
|
[10] Nakao M.: $L^p$ -estimates of solutions of some nonlinear degenerate diffusion equations.J. Math. Soc. Japan 37 (1985), 41-63. Zbl 0584.65073, MR 0769776 |
| Reference:
|
[11] Nečas J.: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[12] Rothe F.: Uniform bounds from bounded $L_p$-functional$ in reaction-diffusion equations.J. Diff. Eqns. 45 (1982), 207-233. MR 0665998 |
| . |
