Existence and nonexistence of global positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary

Authors:
Mingxin Wang and Yonghui Wu

Journal:
Trans. Amer. Math. Soc. **349** (1997), 955-971

MSC (1991):
Primary 35K55, 35K60, 35B35

DOI:
https://doi.org/10.1090/S0002-9947-97-01864-3

MathSciNet review:
1401789

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with the existence and nonexistence of global positive solutions to in ,

and in . Here is a parameter, is a bounded smooth domain. After pointing out the mistakes in *Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary*, SIAM J. Math. Anal. **24** (1993), 317-326, by N. Wolanski, which claims that, for the ball of , the positive solution exists globally if and only if , we reconsider the same problem in general bounded domain and obtain that every positive solution exists globally if and only if .

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Additional Information

**Mingxin Wang**

Affiliation:
Department of Mathematics and Mechanics, Southeast University, Nanjing 210018, P.R. China

Email:
mxwang@seu.edu.cn

**Yonghui Wu**

Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China

DOI:
https://doi.org/10.1090/S0002-9947-97-01864-3

Keywords:
Global solutions,
blow up,
nonlinear diffusion and absorption,
upper and lower solutions

Received by editor(s):
July 13, 1994

Additional Notes:
The first author’s work was supported by The National Natural Science Foundation of China.

Article copyright:
© Copyright 1997
American Mathematical Society