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具耗散项波动方程整体吸引子的有限分形维数 被引量：1

Finite fractal dimensions of global attractors for a class of wave equations with dissipation
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摘要 研究了一类具耗散项的四阶非线性波动方程初边值问题整体吸引子的分形维数.利用偏微分方程的一些标准技巧对非线性项进行估计,在相对较弱的条件下用L轨道法证明了上述问题的整体吸引子具有有限分形维数. The initial boundary value problem and fractal dimensions of global attractors for a class of four order nonlinear wave equations with dissipation are studied.By some standard methods,the nonlinear term is estimated.By L-track technique,it is obtained that the attractors of the above mentioned problem has finite fractal dimensions under rather mild conditions.
作者 张媛媛 王宏伟
机构地区 开封大学数学教研部 安阳师范学院数学与统计学院
出处 《西北师范大学学报（自然科学版）》 CAS 北大核心 2014年第6期11-15,共5页 Journal of Northwest Normal University(Natural Science)
基金 国家自然科学基金资助项目(10971199) 河南省教育厅科学技术研究重点项目(13B110137) 2014年开封市工业科技攻关计划项目(1401012)
关键词 耗散项 波动方程 整体吸引子 L轨道 有限分形维数 dissipation wave equations global attractor L track finite fractal dimension
分类号 O175.29 [理学—基础数学]
  • 相关文献

参考文献11

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共引文献2

同被引文献13

  • 1Wang Mingliang,Zhou Yubin,Li Zhibin.Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Physics Letters A.1996.
  • 2Ma W X, Fuchssteiner E.Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation. International Journal of Non Linear Mechanics. 2012.07 : 231 -232.
  • 3Whitham G B. Variational methods and applications to water waves. Proceedings of the Royal Society of Lon- don.2011.02 : 424-425.
  • 4Matveev VB,Salle MA.Darboux transformations and solitons.2010.11 : 850-852.
  • 5He Ji-huan.A coupling method of homotopy technique and perturbation technique for nonlinear problems. Inter- national Journal of Non Linear Mechanics.2000.
  • 6Davey A,Stewartson K.On three-dimensional packets of surface waves. Proceedings of the Royal Society of London, Series .A (Mathematical and Physical Sciences). 2012.09 : 204-205.
  • 7Kaup D J.A higher-order water-wave equation and the method for solving it. Progress of Theoretical Physics.2013.
  • 8Fan Engui.Extended tanh-function method and its ap- plications to nonlinear equations. Physics Letters. 2012.
  • 9刘明鼎.时滞抛物型方程的拟小波精细积分法[J].长春大学学报,2013,23(4):440-443. 被引量：1
  • 10张媛媛,王宏伟.具耗散项波动方程整体吸引子的有限分形维数[J].扬州大学学报（自然科学版）,2013,16(4):9-12. 被引量：1

引证文献1

西北师范大学学报（自然科学版）
2014年 第6期

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