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一类非线性发展方程的整体吸引子 被引量：3

Global attractor for a class of nonlinear evolution equations
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摘要 本文借助于偏微分方程的一些标准技巧对方程的非线性项进行估计,利用嵌入定理和算子半群的方法得到一类四阶非线性发展方程整体解和吸引子的存在唯一性. In this paper,we studies the existence of the solution and attractor to a class of nonlinear evolution equation.By using some standard methods we estimates the non-linear terms ingeniously.And by applying the method of embedding theorem and semigroup we obtains the existence and uniqueness of the global solution and attractor to a class of nonlinear evolution equations of fourth-order.
作者 张媛媛
机构地区 开封大学数学教研部
出处 《吉林师范大学学报（自然科学版）》 2012年第2期21-28,共8页 Journal of Jilin Normal University:Natural Science Edition
关键词 非线性发展方程 整体解 吸引子 存在唯一性 nonlinear evolution equation global solution attractor existence and uniqueness
分类号 O175.29 [理学—基础数学]
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参考文献9

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同被引文献25

  • 1YANG Zhi-jian. Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation[J]. J Math AnalAppl, 2011, 375(2): 579-593.
  • 2YANG Zhi-jian. Glohal attrator for the Kirehhoff type equation with a strong dissipation[J]. J Differ Eqs, 2010, 249(6): 3258-3278.
  • 3CHUESHOV I, LASIECKA I. Long-time behavior of second order evolution equations with nonlinear damping[J]. Mem Amer Math Soc, 2008, 195(3) : 912-920.
  • 4NAKAO M. An attractor for a nonlinear dissipative wave equation of Kirchhoff type[J]. J Math Appl Anal, 2009, 353(3): 652-659.
  • 5GATTI S, PATA V, ZELIK S. A Gronwall-type lemma with parameter and dissipative estimates for PDEs[J]. Nonlinear Anal, 2009, 70(4): 2337- 2343.
  • 6DELL'ORO F, PATA V. Strongly damped wave equations with critical nonlinearities[J]. Nonlinear Anal, 2012, 75(6): 5723-5735.
  • 7DELL'ORE F, PATA V. Long-term analysis of strongly damped nonlinear wave equations [J]. Nonlinearity, 2011, 24(4): 3413-3435.
  • 8TEMAM R. Infinite Dimensional Dynamical System in Mathematics and Physics [ M]. New York: Springer, 1997: 100-116.
  • 9NAKAO M. Existence of global smooth solution to the initial boundary value problem for the quasi- linearhyperbolic equation with a degenerate dissipative term[J]. J Differ Eqs, 1992, 98(1): 299-327.
  • 10GHISI M. Global solutions for dissipative Kirchhoff strings with non-Lipschitz nonlinear term [J].J Differ Eqs, 2006, 230(1): 128-139.

引证文献3

二级引证文献1

吉林师范大学学报（自然科学版）
2012年 第2期

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