LONG-TIME BEHAVIOR FOR A THERMOELASTIC MICROBEAM PROBLEM WITH TIME DELAY AND THE COLEMAN-GURTIN THERMAL LAW  

作　　者：Wenjun LIU Dongqin CHEN Zhijing CHEN 刘文军;陈冬琴;陈志婧(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China

出　　处：《Acta Mathematica Scientia》2021年第2期609-632,共24页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (11771216 and 11901306);the Key Research and Development Program of Jiangsu Province (Social Development)(BE2019725);the Natural Science Foundation of Jiangsu Province (SBK2017043142)

摘　　要：This study addresses long-time behavior for a thermoelastic microbeam problem with time delay and the Coleman-Gurtin thermal law,the convolution kernel of which entails an extremely weak dissipation in the thermal law.By using the semigroup theory,we first establish the existence of global weak and strong solutions as well as their continuous dependence on the initial data in appropriate function spaces,under suitable assumptions on the weight of time delay term,the external force term and the nonlinear term.We then prove that the system is quasi-stable and has a gradient on bounded variant sets,and obtain the existence of a global attractor whose fractal dimension is finite.A result on the exponential attractor of the system is also proved.

关 键 词：Microbeam problem time delay Coleman-Gurtin law global attractor exponential attractor 

分 类 号：O343.6[理学—固体力学]