EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br#
EQUATIONS IN EXTERIOR DOMAINS

doi:10.1016/S0252-9602(10)60072-0

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 713-725.doi: 10.1016/S0252-9602(10)60072-0

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS

曾宪忠^1|2, 刘振海²

1.Department |of Mathematics and Computational Science, Hunan University |of Science and Technology, |Xiangtan |411201, China；
2.Department |of Mathematics, Central South University, Changsha 410083, China

收稿日期:2007-06-05 出版日期:2010-05-20 发布日期:2010-05-20
基金资助:
This work was supported by the National Natural Science Foundations of China (10971061) and Hunan Provincial Natural Science Foundation of China (09JJ6013)

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS

ZENG Xian-Zhong^1|2, LIU Zhen-Hai²

1.Department |of Mathematics and Computational Science, Hunan University of Science and Technology, |Xiangtan |411201, China；
2.Department |of Mathematics, Central South University, Changsha 410083, China

Received:2007-06-05 Online:2010-05-20 Published:2010-05-20
Supported by:
This work was supported by the National Natural Science Foundations of China (10971061) and Hunan Provincial Natural Science Foundation of China (09JJ6013)

摘要/Abstract

摘要：

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that p_c= (σ+m)n(n-σ-2) is its critical exponent provided {-1, [(1-m)n-2](n+1)} < σ < n-2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Furthermore, we demonstrate that if max{1, σ + m} < p ≤ p_c, then every positive solution of the equations blows up in finite time; whereas for p < p_c, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n ≤ σ + 2.

关键词: Degenerate parabolic equations, exterior domains, inhomogeneous dirichlet boundary conditions, critical exponent, blow-up, global existence

Abstract:

Key words: Degenerate parabolic equations, exterior domains, inhomogeneous dirichlet boundary conditions, critical exponent, blow-up, global existence

中图分类号:

35B33

曾宪忠, 刘振海. EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS[J]. 数学物理学报(英文版), 2010, 30(3): 713-725.

ZENG Xian-Zhong, LIU Zhen-Hai. EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS[J]. Acta mathematica scientia,Series B, 2010, 30(3): 713-725.

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EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS

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