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Title: Boundedness of global solutions for the heat equation with nonlinear boundary conditions (English)
Author: Fila, Marek
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 30
Issue: 3
Year: 1989
Pages: 479-484
Category: math
MSC: 35B40
MSC: 35K05
MSC: 35K60
idZBL: Zbl 0702.35141
idMR: MR1031865
Date available: 2008-06-05T21:39:41Z
Last updated: 2012-04-28
Stable URL:
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Reference: [A2] Amann H.: Parabolic evolution equations and nonlinear boundary conditions.J. Diff. Eqns 72 (1988), 201-269. Zbl 0658.34011, MR 0932367
Reference: [CL] Cazenave T., Lions P. L.: Solutions globales d'équation de la chaleur semilinéaires.Commun. Part. Diff. Equations 9 (1984), 955-978. MR 0755928
Reference: [G] Giga Y.: A bound for global solutions of semilinear heat equations.Commun. Math. Phys. 103 (1986), 415-421. Zbl 0595.35057, MR 0832917
Reference: [F1] Fila M.: Boundedness of global solutions of nonlinear diffusion equations.Preprint Nr. 497 (1988); Univ. Heidelberg. MR 1170469
Reference: [F2] Fila M.: Remarks on blow up for a nonlinear parabolic equation with a gradient term.Preprint Nr. 502 (1989); SFB 123, Univ. Heidelberg. MR 1052569
Reference: [Fo] Filo: Uniform bounds of solutions to a degenerate diffusion equation with nonlinear boundary conditions.Comment. Math. Univ. Carolinae 30 (1989). MR 1031866
Reference: [LP] 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: [NST] 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. MR 0756548
Reference: [PS] Payne L. E., Sattinger D. H.: Saddle points and instability of nonlinear hyperbolic equations.Israel J. Math. 22 (1975), 273-303. MR 0402291


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