EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS 被引量：1

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

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摘要 This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 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. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, 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. This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 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. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, 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.

作者曾宪忠刘振海

机构地区 Department of Mathematics and Computational Science Department of Mathematics

出处《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期713-725,共13页 数学物理学报（B辑英文版）

基金 supported by the National Natural Science Foundations of China(10971061) Hunan Provincial Natural Science Foundation of China (09JJ6013)

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

分类号 O175.26 [理学—基础数学] O175.14 [理学—基础数学]

作者简介 E-mail：zxzh217@sohu.com;xzzeng@hnust.edu.cn

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