Long-Time Behavior for a Thermoelastic Microbeam Problem with Time Delay and the Coleman-Gurtin Thermal Law

  • SCI-E
作者: Wenjun Liu;Dongqin Chen;Zhijing Chen
作者机构: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
语种: 英文
关键词: Microbeam problem;time delay;Coleman-Gurtin law;global attractor;exponential attractor
期刊: Acta Mathematica Scientia
ISSN: 0252-9602
年: 2021
卷: 41
期: 2
页码: 609-632
基金类别: National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11771216, 11901306]; Key Research and Development Program of Jiangsu Province (Social Development) [BE2019725]; Natural Science Foundation of Jiangsu ProvinceNatural 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.

文件格式:
导出字段:
导出
关闭
Long-Time Behavior for a Thermoelastic Microbeam Problem with Time Delay and the Coleman-Gurtin Thermal Law
有问题请联系我们,邮箱:常见的失败原因