Global existence and nonexistence for degenerate parabolic systems

Authors:
Yuxiang Li, Weibing Deng and Chunhong Xie

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3661-3670

MSC (2000):
Primary 35K50, 35K55, 35K65

DOI:
https://doi.org/10.1090/S0002-9939-02-06630-3

Published electronically:
May 14, 2002

MathSciNet review:
1920046

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Abstract | References | Similar Articles | Additional Information

Abstract: The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system

in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .

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Additional Information

**Yuxiang Li**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
lieyuxiang@yahoo.com.cn

**Weibing Deng**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

**Chunhong Xie**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9939-02-06630-3

Keywords:
Global existence,
global nonexistence,
degenerate parabolic system

Received by editor(s):
July 23, 2001

Published electronically:
May 14, 2002

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2002
American Mathematical Society