具源项和阻尼项发展方程整体吸引子的Hausdorff维数  

Hausdorff dimensions of global attractors to a class of evolution equations with source and damping term

作　　者：张媛媛[1] ZHANG Yuanyuan(Teaching and Research Department of Mathematics,Kaifeng University,Kaifeng 475000,Chin)

机构地区：[1]开封大学数学教研部,河南开封475000

出　　处：《安徽大学学报（自然科学版）》2018年第4期32-39,共8页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10971199);河南省高等学校重点科研项目(18B110013);开封市科技计划项目(1708008;1808007)

摘　　要：研究一类具源项和阻尼项的发展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较弱的条件下上述问题的整体吸引子具有Hausdorff维数.The author studied the behaviors of the global attractors to a class of evolution equations with damping and source term. By using some standard methods, the non-linear terms were estimated. By applying embedding theorem and the method of semigroup, it proved that under rather mild conditions the attractors to the above-mentioned problem had Hausdorff dimensions.

关 键 词：源项 阻尼项 发展方程 整体吸引子 HAUSDORFF维数 

分 类 号：O175.29[理学—数学]