Boundedness of global solutions for the heat equation with nonlinear boundary conditions

Marek Fila

Commentationes Mathematicae Universitatis Carolinae (1989)

  • Volume: 030, Issue: 3, page 479-484
  • ISSN: 0010-2628

How to cite

top

Fila, Marek. "Boundedness of global solutions for the heat equation with nonlinear boundary conditions." Commentationes Mathematicae Universitatis Carolinae 030.3 (1989): 479-484. <http://eudml.org/doc/17761>.

@article{Fila1989,
author = {Fila, Marek},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {blow-up; heat equation; nonlinear boundary condition; global solutions},
language = {eng},
number = {3},
pages = {479-484},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Boundedness of global solutions for the heat equation with nonlinear boundary conditions},
url = {http://eudml.org/doc/17761},
volume = {030},
year = {1989},
}

TY - JOUR
AU - Fila, Marek
TI - Boundedness of global solutions for the heat 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 - 479
EP - 484
LA - eng
KW - blow-up; heat equation; nonlinear boundary condition; global solutions
UR - http://eudml.org/doc/17761
ER -

References

top
  1. Amann H., Quasilinear parabolic systems under nonlinear boundary conditions, Arch. Rat. Mech. Anal. 92 (1986), 153-192. (1986) Zbl0596.35061MR0816618
  2. Amann H., Parabolic evolution equations and nonlinear boundary conditions, J. Diff. Eqns 72 (1988), 201-269. (1988) Zbl0658.34011MR0932367
  3. Cazenave T., Lions P. L., Solutions globales d'équation de la chaleur semilinéaires, Commun. Part. Diff. Equations 9 (1984), 955-978. (1984) Zbl0555.35067MR0755928
  4. Giga Y., A bound for global solutions of semilinear heat equations, Commun. Math. Phys. 103 (1986), 415-421. (1986) Zbl0595.35057MR0832917
  5. Fila M., Boundedness of global solutions of nonlinear diffusion equations, Preprint Nr. 497 (1988); Univ. Heidelberg. (1988) Zbl0764.35010MR1170469
  6. Fila M., Remarks on blow up for a nonlinear parabolic equation with a gradient term, Preprint Nr. 502 (1989); SFB 123, Univ. Heidelberg. (1989) Zbl0768.35047MR1052569
  7. Filo, Uniform bounds of solutions to a degenerate diffusion equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989). (1989) Zbl0702.35142MR1031866
  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. Ni W. M., Sacks P. E., Tavantzis J. E., On the asymptotic behavior of solutions of certain quasilinear equation of parabolic type, J. Diff. Eqns 54 (1984), 97-120. (1984) Zbl0565.35053MR0756548
  10. Payne L. E., Sattinger D. H., Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303. (1975) Zbl0317.35059MR0402291

Citations in EuDML Documents

top
  1. Ján Filo, Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions
  2. Gary Lieberman, Study of global solutions of parabolic equations via a priori estimates III. Equations of p-Laplacian type
  3. Bei Hu, Hong-Ming Yin, On critical exponents for the heat equation with a nonlinear boundary condition
  4. Marek Fila, Ján Filo, Blow-up on the boundary: a survey
  5. Miroslav Chlebík, Marek Fila, Some recent results on blow-up on the boundary for the heat equation

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.