Geodesic
Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions
Commentationes Mathematicae Universitatis Carolinae, Tome 30 (1989) no. 3, pp. 485-495 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 35K05, 35K55, 35K60 
@article{CMUC_1989_30_3_a7,
     author = {Filo, J\'an},
     title = {Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {485--495},
     year = {1989},
     volume = {30},
     number = {3},
     mrnumber = {1031866},
     zbl = {0702.35142},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1989_30_3_a7/}
}
TY  - JOUR
AU  - Filo, Ján
TI  - Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1989
SP  - 485
EP  - 495
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_1989_30_3_a7/
LA  - en
ID  - CMUC_1989_30_3_a7
ER  - 
%0 Journal Article
%A Filo, Ján
%T Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions
%J Commentationes Mathematicae Universitatis Carolinae
%D 1989
%P 485-495
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_1989_30_3_a7/
%G en
%F CMUC_1989_30_3_a7
Filo, Ján. Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions. Commentationes Mathematicae Universitatis Carolinae, Tome 30 (1989) no. 3, pp. 485-495. http://geodesic.mathdoc.fr/item/CMUC_1989_30_3_a7/

[1] Alikakos N. D.: $L^p$ bounds of solutions of reaction-diffusion equations. Comm. Partial Differential Equations 4 (1979), 827-868. | MR

[2] Amann H.: Quasilinear parabolic systems under nonlinear boundary conditions. Arch. Rat. Mech. Anal. 92 (1986), 153-192. | MR | Zbl

[3] DiBenedetto E.: Continuity of weak solutions to a general porous medium equation. Indiana Univ. Math. J. 32 (1983), 83-118. | MR | Zbl

[4] Fila M.: Boundedness of global solutions for the heat equation with nonlinear boundary conditions. Comment. Math. Univ. Carolinae 30 (1989), 479-484. | MR | Zbl

[5] Filo J.: $L^∞$-estimate for nonlinear diffusion equations. manuscript. | Zbl

[6] Friedman A., McLeod B.: Blow-up of positive aolutiona of aemilinear heat equations. Indiana Univ. Math. J. 34 (1985), 425-447. | MR

[7] Ladyzhenskaya O. A., Solonikov V. A., Uraltseva N. N.: Linear and Quasi-linear Equations of Parabolic Type. Nauka, Moscow, 1967.

[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

[9] Nakao M.: Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations. Nonlinear Analysis 10 (1986), 299-314. | MR | Zbl

[10] Nakao M.: $L^p$ -estimates of solutions of some nonlinear degenerate diffusion equations. J. Math. Soc. Japan 37 (1985), 41-63. | MR | Zbl

[11] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. | MR

[12] Rothe F.: Uniform bounds from bounded $L_p$-functional$ in reaction-diffusion equations. J. Diff. Eqns. 45 (1982), 207-233. | MR