On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
Commentationes Mathematicae Universitatis Carolinae (1999)
- Volume: 40, Issue: 3, page 457-475
- ISSN: 0010-2628
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topBoni, Théodore K.. "On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 457-475. <http://eudml.org/doc/248398>.
@article{Boni1999,
abstract = {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.},
author = {Boni, Théodore K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {blow-up; global existence; asymptotic behavior; maximum principle; blow-up time; global existence; blow-up sets; maximum principle},
language = {eng},
number = {3},
pages = {457-475},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions},
url = {http://eudml.org/doc/248398},
volume = {40},
year = {1999},
}
TY - JOUR
AU - Boni, Théodore K.
TI - On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 457
EP - 475
AB - 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.
LA - eng
KW - blow-up; global existence; asymptotic behavior; maximum principle; blow-up time; global existence; blow-up sets; maximum principle
UR - http://eudml.org/doc/248398
ER -
References
top- 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. (1998) Zbl0913.35069MR1648453
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- Egorov Yu.V., Kondratiev V.A., On blow-up solutions for parabolic equations of second order, in `Differential Equations, Asymptotic Analysis and Mathematical Physics', Berlin, Academie Verlag, 1997, pp.77-84. Zbl0879.35081MR1456179
- Friedman A., McLeod B., Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447. (1985) Zbl0576.35068MR0783924
- Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, NJ, 1967. Zbl0549.35002MR0219861
- 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. Zbl0924.35017MR1739446
- Walter W., Differential-und Integral-Ungleichungen, Springer, Berlin, 1964. Zbl0119.12205MR0172076
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