Timoshenko系统在Gurtin-Pipkin热能定律下解的整体存在性、渐进性及一致吸引子

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  • College of Science,Donghua University
ZHENG Xiu-zhen(1991-), female, native of Longyan, Fujian, a master candidate of Donghua University, engages in nonlinear evolution equations and in¯nite-dimensional dynamical systems.

收稿日期: 2016-03-20

  网络出版日期: 2020-11-05

基金资助

Supported by the National Natural Science Foundation of China(11271066); Supported by the Shanghai Education Commission(13ZZ048);

Global Existence, Asymptotic Behavior and Uniform Attractors of Timoshenko Systems with Gurtin-Pipkin Thermal Law

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  • College of Science,Donghua University
ZHENG Xiu-zhen(1991-), female, native of Longyan, Fujian, a master candidate of Donghua University, engages in nonlinear evolution equations and in¯nite-dimensional dynamical systems.

Received date: 2016-03-20

  Online published: 2020-11-05

Supported by

Supported by the National Natural Science Foundation of China(11271066); Supported by the Shanghai Education Commission(13ZZ048);

摘要

In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method. 

本文引用格式

郑秀珍 . Timoshenko系统在Gurtin-Pipkin热能定律下解的整体存在性、渐进性及一致吸引子[J]. 数学季刊, 2016 , 31(3) : 307 -330 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.03.009

Abstract

In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method. 
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