强阻尼高阶Kirchhoff方程的整体吸引子族及其维数估计  

Global Attractor Family and Its Dimension Estimation for Higher-Order Kirchhoff Type Equation with Strong Damping

作　　者：林国广[1] 官丽萍 LIN Guoguang;GUAN Liping(School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)

机构地区：[1]云南大学数学与统计学院

出　　处：《应用泛函分析学报》2019年第3期268-281,共14页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11561076)

摘　　要：研究了带有非线性强阻尼项的高阶Kirchhoff型方程的初边值问题.在对Kirchhoff应力项,二阶非线性源项的适当假设条件下,首先利用先验估计,Galerkin方法得到了整体解的存在唯一性,并由先验估计构造了有界吸收集及解半群的全连续性,证明了整体吸引子族的存在性;其次通过线性化方程及解半群的Frechet可微性,获得整体吸引子族的Hausdorff维数及Fractal维数的有限维估计.The initial-boundary value problem for higher-order Kirchhoff equation with strong non-linear damping term is studied.Under the appropriate assumption of Kirchhoff stress term and second-order non-linear source term,the existence and uniqueness of global solutions are obtained by using prior estimation and Galerkin method,and the bounded absorption set and solution semigroup are constructed by prior estimation.The existence of the global attractor family is proved by its complete continuity.Secondly,the Hausdorff dimension and the fractal dimension of the global attractor family are estimated by linearization equation and Frechet differentiability of the solution semigroup.

关 键 词：高阶Kirchhoff方程 整体吸引子族 HAUSDORFF维数 Fractal维数 

分 类 号：O175.29[理学—数学]