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齐次Neumann边界条件下反应扩散方程的零维全局吸引子 被引量:1

Zero-dimensional Global Attractor for Reaction-diffusion Equations with Homogeneous Neumann Boundary Condition
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摘要 通过渐近自治微分方程的极限集的性质,证明了在一定的参数范围内,齐次Neumann边界条件下反应扩散方程存在零维全局吸引子,且该吸引子是一条线段. By the property of limit set of asymptotic autonomous differential equations, proved that in certain parameter region, the reaction-diffusion equation has a zero-dimensional global attractor, which is a line segment.
作者 李红艳
出处 《河北师范大学学报(自然科学版)》 CAS 北大核心 2008年第3期292-294,共3页 Journal of Hebei Normal University:Natural Science
基金 国家自然科学基金(10771139) 上海高校选拔培养优秀青年教师基金(gjd-07011) 上海市曙光计划基金(06SG54) 上海市科委科技攻关重点项目(065111037) 上海工程技术大学重点学科项目(E694-xk0704)
关键词 反应扩散方程 全局吸引子 线段 reaction-diffusion equations global attractor line segment
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参考文献6

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  • 2TEMAM R. Infinite-dimensional Dynamical Systems in Mechanics and Physics [M]. 2nd Edition. New York:Spring-verlag, 1997.
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同被引文献9

  • 1叶其孝.反应扩散方程简介.知识与进展,1984,:48-56.
  • 2TEMAM R. Infinite-dimensional Dynamical Systems in Mechanics and Physics[M]. 2nd Edition. New York: Spring-verlag,1997.
  • 3CHEPYZHOV V V ,VISHIK M I. Attractor of Equations of Mathematical Physics[M]. Amer Math Soc Province,2002.
  • 4HALE J. Asymptotic Behavior of Dissipative Systems[M]. Rhode Island: Amer Math Soc Province,1988.
  • 5BABIN A V ,VISHIK M I. Attractors of Evolution Equations[M]. Amsterdam: North2Holland,1992.
  • 6Eden A, Foias C, Nicolaenko B, Temam R. Exponential Attractors for Dissipative Evolution Equa- tions[M]. New York:Masson.Paris: Wiely, 1994.
  • 7Liu Y F, MA Q Z. Exponential attractors for a nonclassical diffusion equation[J]. Elec J Diff Equa, 2009: 1-7.
  • 8刘永锋.一类模式演化方程的指数吸引子[J].数学教学研究,2010,29(2):45-47. 被引量:1
  • 9马巧珍,刘永锋.非线性项任意次多项式增长时非经典反应扩散方程的指数吸引子(英文)[J].工程数学学报,2011,28(1):134-138. 被引量:3

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