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具强阻尼项波动方程整体吸引子的Hausdorff维数

Hausdorff Dimensions of Global Attractors for a Class of Strongly Damped Wave Equations
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摘要 研究了一类具强阻尼项的波动方程整体吸引子的性质.借助偏微分方程的一些标准技巧对非线性项进行估计,利用嵌入定理和算子半群的方法证明了在相对比较弱的条件下上述问题的整体吸引子具有Hausdorff维数. The behavior of the global attractors for a class of strongly damped wave equations was studied.By some standard methods the nonlinear term was estimated.By embedding theorem and the method of semigroup,it was obtained that under rather mild conditions the attractors of the above-mentioned problem had Hausdorff dimensions.
作者 张媛媛 达芳
机构地区 开封大学数学教研部 郑州大学数学系
出处 《郑州大学学报（理学版）》 CAS 北大核心 2012年第4期20-25,共6页 Journal of Zhengzhou University:Natural Science Edition
基金 国家自然科学基金资助项目 编号10971199
关键词 波动方程 整体吸引子 HAUSDORFF维数 wave equation global attractor Hausdorff dimension
分类号 O175.29 [理学—基础数学]
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参考文献4

  • 1张媛媛.一类非线性发展方程的整体吸引子[J].吉林师范大学学报（自然科学版）,2012,33(2):21-28. 被引量：3
  • 2Nakao M. Existence of global smooth solution to the initial boundary value problem for the quasi-linear hyperbolic equation with a degenerate dissipative term[J].Differential Equations,1992,(01):299-327.
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  • 4Ghidaglia J M. Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional system in the long time[J].Differential Equations,1988,(02):369-390.

二级参考文献9

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共引文献2

郑州大学学报（理学版）
2012年 第4期

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