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Remarks on blow-up behavior for a nonlinear diffusion equation with Neumann boundary conditions
Author(s):
Keng
Deng;
Mingxi
Xu
Journal:
Proc. Amer. Math. Soc.
127
(1999),
167-172.
MSC (1991):
Primary 35B40, 35K20, 35K55
MathSciNet review:
1485467
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Abstract:
We establish the blow-up rate for the solution of a nonlinear diffusion equation  , subject to Neumann boundary conditions  .
References:
- [1]
- K. Deng, The blow-up behavior of the heat equation with Neumann boundary conditions, J. Math. Anal. Appl. 188 (1994), 641-650. MR 95i:35120
- [2]
- K. Deng and M. Xu, On solutions of a singular diffusion equation, preprint.
- [3]
- M. Fila and H.A. Levine, Quenching on the boundary, Nonlinear Anal. TMA 21 (1993), 795-802. MR 95b:35028
- [4]
- M. Fila and P. Quittner, The blow-up rate for the heat equation with a non-linear boundary condition, Math. Methods Appl. Sci. 14 (1991), 197-205. MR 92a:35023
- [5]
- J. Filo, Diffusivity versus absorption through the boundary, J. Differential Equations 99 (1992), 281-305. MR 94d:35083
- [6]
- J.L. Gómez, V. Márquez, and N. Wolanski, Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition, J. Differential Equations 92 (1991), 384-401. MR 92j:35098
- [7]
- B. Hu and H.-M. Yin, The profile near blow-up time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc.
 (1994), 117-135. MR 95c:35040 - [8]
- N. Wolanski, Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary,SIAM J. Math. Anal. 24 (1993), 317-326. MR 93j:35023
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Additional Information:
Keng
Deng
Affiliation:
Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana 70504
Email:
kxd5858@usl.edu
Mingxi
Xu
Affiliation:
Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana 70504
Email:
mxx3473@usl.edu
DOI:
10.1090/S0002-9939-99-04748-6
PII:
S 0002-9939(99)04748-6
Received by editor(s):
May 6, 1997
Communicated by:
Jeffrey B. Rauch
Copyright of article:
Copyright
1999,
American Mathematical Society
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