Global existence and nonexistence for degenerate parabolic systems
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- by Yuxiang Li, Weibing Deng and Chunhong Xie
- Proc. Amer. Math. Soc. 130 (2002), 3661-3670
- DOI: https://doi.org/10.1090/S0002-9939-02-06630-3
- Published electronically: May 14, 2002
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Abstract:
The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system \[ \begin {split} u_t=v^p(\Delta u+au), v_t=u^q(\Delta v+bv) \end {split} \] in the cylinder $\Omega \times (0,\infty )$, where $\Omega \subset R^N$ is bounded and $p, q, a, b$ are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by $\lambda _1$ the first Dirichlet eigenvalue for the Laplacian on $\Omega$. We prove that there exists a global solution iff $\lambda _1\geq \min \{a,b\}$.References
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Bibliographic Information
- Yuxiang Li
- Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
- MR Author ID: 699784
- 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
- Received by editor(s): July 23, 2001
- Published electronically: May 14, 2002
- Communicated by: David S. Tartakoff
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1920046