| 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:
|
http://hdl.handle.net/10338.dmlcz/119102 |
| . |
| 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 |
| Reference:
|
[2] Chipot M., Fila M., Quittner P.: Stationary solutions, blow-up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions.Acta Math. Univ. Comenianae, Vol. LX, 1 (1991), 35-103. Zbl 0743.35038, MR 1120596 |
| Reference:
|
[3] 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. 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 |
| . |
