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带有导数项的反应扩散方程指数吸引子存在性的一个注解 被引量：3

A Remark of Existence of Exponential Attractors for a Reaction-diffusion Equation with Distribution Derivatives
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摘要 利用加强的平坦性条件,证明了带有导数项的反应扩散方程当非线性项f任意阶多项式增长时,指数吸引子的存在性. The paper establishes the existence of exponential attractors for a reaction-diffusion equation with distribution derivatives by a method of enhanced flattening property when nonlinear term is a polynomial growth of arbitrary order.
作者 王晓萍
机构地区 西北师范大学数学与统计学院
出处 《兰州文理学院学报（自然科学版）》 2015年第6期23-25,共3页 Journal of Lanzhou University of Arts and Science(Natural Sciences)
基金 国家自然科学基金项目(11561064) 甘肃省自然科学基金项目(1107RJZA223)
关键词 反应扩散方程 导数项 指数吸引子 加强的平坦性条件 reaction-diffusion equation distribution derivatives exponential attractor enhanced flattening property
分类号 O175.29 [理学—基础数学]
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参考文献8

  • 1TEMAM R. Infinite-dimensional dynamical systems in mechanics and physics[M]. Berlin: Springer-Verlag, 1997.
  • 2MARION M. Attractors for reaction-diffusion equa- tion: existence and estimate of their dimension[J]. Appl Anal, 1987,25 : 101-147.
  • 3MARION M. Approximate inertial manifolds for re- action-diffusion equation in high space dimension[J]. Dynan Differential Equations, 1989 ( 1 ) : 245-267.
  • 4ROBINSON J C. Infinite-dimensional dynamical sys- tems an Tndouction to Dissipative Parabolic PDEs and the Theory of Global Attractors [M]. Cambridge : Cambridge University Press, 2001.
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  • 6ZHONGC K, YANG M H, SUN C Y. The exist- ence of global attractors for the norm-to-weak conti- nus semigroup and application to the nonlinear reac- tion-diffusion equation [J]. Differential Equations, 2006 (223) : 367-399.
  • 7康亚虎,马巧珍.具有导数项的非线性反应扩散方程指数吸引子的存在性[J].系统科学与数学,2012,32(11):1407-1412. 被引量：5
  • 8SUN C Y,ZHONG C K. Attractors for the semilin- ear reaction-diffusion equation with distribution de- rivatives in unbounded domains[J]. Nonlinear Anal, 2005(63) :49-65.

二级参考文献11

  • 1Bear J. Dynamics of Fluids in Porous Media. New York: American Elsevericer Pubishing Company, Inc, 197"2.
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  • 8Efendiev M, Miranville A. Expontential attractors for a nonlinear reaction-diffusion systems in R3. C. R. Acad. Sci. Paris Ser. I Math., 2000, 330(8): 713-718.
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  • 10Eden A, Foias C, Temam R. Exponential Attractors for Dissipative Evolution Equations. New York: Masson Paris Wiely, 1994.

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兰州文理学院学报（自然科学版）
2015年 第6期

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