数学季刊 >

2017 , Vol. 32 >Issue 3: 305 - 321

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.03.009

关于衰减Timoshenko系统的解的整体存在性、渐近性及一致吸引子

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  •  College of Science, Donghua University.  Department of Applied Mathematics, Donghua University
HU Wen-song(1990-), female, native of Anqing, Anhui, a master candidate of Donghua University, engages in nonlinear evolution equations and in¯nite-dimensional dynamical systems.

收稿日期: 2016-11-16

  网络出版日期: 2020-10-22

基金资助

Supported by the National Natural Science Foundation of China(11671075)；

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Global Existence, Asymptotic Behavior and Uniform Attractors for Damped Timoshenko Systems

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  •  College of Science, Donghua University.  Department of Applied Mathematics, Donghua University
HU Wen-song(1990-), female, native of Anqing, Anhui, a master candidate of Donghua University, engages in nonlinear evolution equations and in¯nite-dimensional dynamical systems.

Received date: 2016-11-16

  Online published: 2020-10-22

Supported by

Supported by the National Natural Science Foundation of China(11671075)；

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摘要

In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets. 

关键词： Timoshenko systems; global existence; semigroup methods; asymptotic behavior; uniform attractors

本文引用格式

胡文松, 秦玉明 . 关于衰减Timoshenko系统的解的整体存在性、渐近性及一致吸引子[J]. 数学季刊, 2017 , 32(3) : 305 -321 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.03.009

Abstract

In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets. 

Key words： Timoshenko systems; global existence; semigroup methods; asymptotic behavior; uniform attractors

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