Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions

Ján Filo

Commentationes Mathematicae Universitatis Carolinae (1989)

  • Volume: 030, Issue: 3, page 485-495
  • ISSN: 0010-2628

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Filo, Ján. "Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions." Commentationes Mathematicae Universitatis Carolinae 030.3 (1989): 485-495. <http://eudml.org/doc/17762>.

@article{Filo1989,
author = {Filo, Ján},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {parabolic equations; nonlinear boundary conditions; - estimate; degenerate diffusion equation; heat equation},
language = {eng},
number = {3},
pages = {485-495},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions},
url = {http://eudml.org/doc/17762},
volume = {030},
year = {1989},
}

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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 030
IS - 3
SP - 485
EP - 495
LA - eng
KW - parabolic equations; nonlinear boundary conditions; - estimate; degenerate diffusion equation; heat equation
UR - http://eudml.org/doc/17762
ER -

References

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  1. Alikakos N. D., L p bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations 4 (1979), 827-868. (1979) Zbl0421.35009MR0537465
  2. Amann H., Quasilinear parabolic systems under nonlinear boundary conditions, Arch. Rat. Mech. Anal. 92 (1986), 153-192. (1986) Zbl0596.35061MR0816618
  3. DiBenedetto E., Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 (1983), 83-118. (1983) Zbl0526.35042MR0684758
  4. Fila M., Boundedness of global solutions for the heat equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989), 479-484. (1989) Zbl0702.35141MR1031865
  5. Filo J., L -estimate for nonlinear diffusion equations, manuscript. Zbl0849.35061
  6. Friedman A., McLeod B., Blow-up of positive aolutiona of aemilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447. (1985) MR0783924
  7. Ladyzhenskaya O. A., Solonikov V. A., Uraltseva N. N., Linear and Quasi-linear Equations of Parabolic Type, Nauka, Moscow, 1967. (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. (1974) MR0470481
  9. Nakao M., Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations, Nonlinear Analysis 10 (1986), 299-314. (1986) Zbl0595.35058MR0834507
  10. Nakao M., L p -estimates of solutions of some nonlinear degenerate diffusion equations, J. Math. Soc. Japan 37 (1985), 41-63. (1985) Zbl0584.65073MR0769776
  11. Nečas J., Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  12. Rothe F., [unknown], J. Diff. Eqns. 45 (1982), 207-233. (1982) MR0665998

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