Kirchhoff吊桥方程解的长时间行为  

Long-time Behavior of Solution for Kirchhoff Suspension Bridge Equations

作　　者：姚莉娟 马巧珍 Li Juan YAO;Qiao Zhen MA(College of Mathematics a/nd Statistics,Northwest Normal University,Lanzhou 730070,P.R.China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学学报（中文版）》2022年第3期499-512,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11961059;11761062)。

摘　　要：利用Faedo-Galerkin方法获得了问题弱解和强解的存在唯一性及解对初值的连续依赖性,并运用有界吸收集的存在性刻画了与问题相关的动力系统(X_(0),S(t))的耗散性.当非线性阻尼项|u_(t)|^(p)u_(t)中的p>0时,证明了动力系统(X_(0),S(t))的渐近光滑性;而当p=0时,得到了动力系统(X_(0),S(t))的拟稳定性.基于上面的结论,获得了具有多项式阻尼项和多项式非线性项的基尔霍夫型吊桥方程有限维全局吸引子和广义指数吸引子的存在性.本文推广和部分改进了以往的一些结果.We first obtain the existence and uniqueness of the both weak and strong solutions by using the Faedo-Galerkin method,as well as the continuous dependence on initial values.Then the existence of a bounded absorbing set is used to characterize the dissipativity of the dynamical system(X_(0),S(t))associated with the problem.Next the asymptotic smoothness of the dynamical system(X_(0),S(t))is demonstrated when p>0 in the nonlinear damping term |u_(t)|^(p)u_(t);and while p=0 we get the quasi-stability of(X_(0),S(t)).Finally,based on the above conclusions,we achieve the existence of the finite dimensional global attractor and the generalized exponential attractor for Kirchhoff type suspension bridge equations with polynomial damping and polynomial nonlinearity.We extend and partially improve the results of published theses before in this paper.

关 键 词：吊桥方程 吸引子 多项式阻尼 多项式非线性项 

分 类 号：O175.29[理学—数学]