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Title: On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions (English)
Author: Boni, Théodore K.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 40
Issue: 3
Year: 1999
Pages: 457-475
Category: math
Summary: We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as $t\rightarrow\infty$. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set. (English)
Keyword: blow-up
Keyword: global existence
Keyword: asymptotic behavior
Keyword: maximum principle
MSC: 35B40
MSC: 35K55
MSC: 35K60
idZBL: Zbl 1011.35078
idMR: MR1732489
Date available: 2009-01-08T18:54:11Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Boni T.K.: Sur l'explosion et le comportement asymptotique de la solution d'une équation parabolique semi-linéaire du second ordre.C.R. Acad. Paris, t. 326, Série I, 1 (1998), 317-322. Zbl 0913.35069, MR 1648453
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Reference: [3] Egorov Yu.V., Kondratiev V.A.: On blow-up solutions for parabolic equations of second `Differential Equations, Asymptotic Analysis and Mathematical Physics', Berlin, Academie Verlag, 1997, pp.77-84. Zbl 0879.35081, MR 1456179
Reference: [4] Friedman A., McLeod B.: Blow-up of positive solutions of semilinear heat equations.Indiana Univ. Math. J. 34 (1985), 425-447. Zbl 0576.35068, MR 0783924
Reference: [5] Protter M.H., Weinberger H.F.: Maximum Principles in Differential Equations.Prentice Hall, Englewood Cliffs, NJ, 1967. Zbl 0549.35002, MR 0219861
Reference: [6] Rossi J.D.: The blow-up rate for a semilinear parabolic equation with a nonlinear boundary condition.Acta Math. Univ. Comenianae, Vol. LXVII, 2 (1998), 343-350. Zbl 0924.35017, MR 1739446
Reference: [7] Walter W.: Differential-und Integral-Ungleichungen.Springer, Berlin, 1964. Zbl 0119.12205, MR 0172076


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