非柱形区域上时滞p-Laplace方程解的长时间行为  

Long Time Behavior of Solutions to Delayed P-Laplace Equation in a Noncylindrical Region

作　　者：李心 王春燕 Li Xin;Wang Chunyan(School of Science,YanShan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《河南科技大学学报（自然科学版）》2023年第3期96-104,I0007,共10页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11801493);河北省自然科学基金项目(A2022203004,A2018203309);河北省教育厅高等学校科技计划青年基金项目(QN2020203)。

摘　　要：为了深入研究微分动力系统中p-Laplace方程的性质,讨论一类定义在同胚区域上带有时滞项的p-Laplace方程的长时间性态问题。首先,为了克服非柱形区域上区域随时间变化带来的困难,利用同胚坐标变换将非柱形区域转换成柱形区域,并建立柱形区域上的一系列先验估计;随后,通过Faedo-Galerkin方法得到系统弱解的适定性结果;最后,利用能量方法证明系统的渐近紧性。结果表明:所讨论的非柱形区域上带时滞的p-Laplace方程存在唯一的拉回吸引子。In order to study the properties of P-Laplace equation in differential dynamical systems,a class of long time behavior problems of P-Laplace equation with delay term defined in homeomorphic region was discussed.Firstly,in order to overcome the difficulty caused by the time change of the region on the noncylindrical region,the homeomorphic coordinate transformation was used to convert the non-cylindrical region into the columnar region,and a series of prior estimates were built on the columnar region.Then,the fittest results of the weak solutions of the system were obtained by the Faedo-Galerkin method.Finally,the asymptotic compactness of the system was proved by the energy method.The results show that there is a unique pullback attractor for the P-Laplace equation with delay in the noncylindrical region.

关 键 词：微分动力系统 非柱形区域 P-LAPLACE方程 时滞项 弱解 拉回吸引子 

分 类 号：O175.2[理学—数学]