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

Commentationes Mathematicae Universitatis Carolinae (1989)

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

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topFila, 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

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- Amann H., Parabolic evolution equations and nonlinear boundary conditions, J. Diff. Eqns 72 (1988), 201-269. (1988) Zbl0658.34011MR0932367
- Cazenave T., Lions P. L., Solutions globales d'équation de la chaleur semilinéaires, Commun. Part. Diff. Equations 9 (1984), 955-978. (1984) Zbl0555.35067MR0755928
- Giga Y., A bound for global solutions of semilinear heat equations, Commun. Math. Phys. 103 (1986), 415-421. (1986) Zbl0595.35057MR0832917
- Fila M., Boundedness of global solutions of nonlinear diffusion equations, Preprint Nr. 497 (1988); Univ. Heidelberg. (1988) Zbl0764.35010MR1170469
- 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
- Filo, Uniform bounds of solutions to a degenerate diffusion equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989). (1989) Zbl0702.35142MR1031866
- 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
- 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
- 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- Ján Filo, Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions
- Gary Lieberman, Study of global solutions of parabolic equations via a priori estimates III. Equations of p-Laplacian type
- Bei Hu, Hong-Ming Yin, On critical exponents for the heat equation with a nonlinear boundary condition
- Marek Fila, Ján Filo, Blow-up on the boundary: a survey
- Miroslav Chlebík, Marek Fila, Some recent results on blow-up on the boundary for the heat equation

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