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非线性边界条件下抛物问题解的爆破 被引量：1

Blow-up of Solutions of Parabolic Problems with Nonlinear Boundary Conditions
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摘要 本文讨论在在非线性边界条件下反应-扩散方程解的爆破.当非线性项f,g满足一定的条件时,我们得到其解在有限时间内爆破. The purpose of this paper is to investigate the blow-up solutions of reactiondiffusion equations with nonlinear boundary conditions. Under some assumptions on the nonlinear terms f and g, we show that the solutions blow up in finite time.
作者 李晓军 钟承奎
机构地区 河海大学理学院 兰州大学数学与统计学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2007年第5期981-988,共8页 Acta Mathematica Sinica：Chinese Series
关键词 反应-扩散 非线性边界条件 爆破 Reaction-diffusion nonlinear boundary condition blow-up
分类号 O175.26 [理学—基础数学]
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  • 1Acosta, C., Rossi, J. D.: Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition. Z. Angew. Math. Phys., 48, 711-724 (1997).
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同被引文献7

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  • 2AMANN H. Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems [ J]. Function Space, Differential Operators and Nonlinear Analysis, Text Sur Mathematik ( Teubner ), 1993,133 : 9-126.
  • 3LI Xiao-jun. The blow-up and asymptotic behavior of the solutions of parabolic problems with nonlinear boundary conditions[ D]. Lanzhou: Lanzhou University, 2005.
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  • 5ARRIETA J M, CARVALHO A N, RODRIGUEZ-BERNAL A. Parabolic problems with nonlinears boundary conditions and critical nonlinearities[ J]. J Differential Equations, 1999,156: 376-406.
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  • 7RODRIGUEZ-BERNAL A. Attractors for parabolic equations with nonlinear boundary conditions, critical exponents, and singular initial data [J] .J Differential Equations,2002,181 : 165-196.

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数学学报（中文版）
2007年 第5期

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