两类热弹耦合梁方程组的整体吸引子
发布时间：2018-08-28 19:00
【摘要】：热弹耦合梁方程是根据梁的变形规律以及温度分布规律建立的数学模型,这类模型渗透在自然科学的各个领域,有实际的研究背景.本文主要探究了非自治热弹耦合梁整体吸引子存在性问题,包括具有双记忆项的热弹耦合梁方程组的初边值问题以及具有记忆项和强阻尼项的热弹耦合梁方程组的初边值问题,首先将非自治系统转化为自治系统,应用半群理论证明了解的适定性定理,其次利用经典积分估计方法证明系统对应的无穷维动力系统存在有界吸收集,最后利用经典积分估计方法方法证明系统对应的解半群的渐近紧性,进而得到系统整体吸引子的存在性.全文结构如下:第一章:简要介绍了热弹耦合梁方程组的研究背景和现状,同时概述了本文的主要工作和主要结果.第二章:介绍了本文用到的基础知识,包括基本空间、引理、概念、假设以及一些常用的不等式.第三章:证明了具有双记忆项的热弹耦合梁方程组整体解的存在性以及整体吸引子的存在性.第四章:证明了具有记忆项和强阻尼项的热弹耦合梁方程组整体吸引子的存在性。
[Abstract]:Thermoelastic coupling beam equation is a mathematical model based on the law of deformation and temperature distribution of the beam. This kind of model permeates every field of natural science and has practical research background. This paper mainly discusses the existence of global attractor for non-autonomous thermoelastic coupling beam, including the equations of thermoelastic coupling beam with two memory terms. The initial-boundary value problem and the initial-boundary value problem for a thermoelastic coupled beam system with memory term and strong damping term are first transformed into an autonomous system. The well-posedness theorem of the solution is proved by using semigroup theory. Then the existence of bounded absorption sets for the corresponding infinite-dimensional dynamical systems is proved by using classical integral estimation method. By using the classical integral estimation method, the asymptotic compactness of the solution semigroup of the system is proved, and the existence of the global attractor of the system is obtained. The basic knowledge used includes basic space, lemma, concepts, assumptions and some inequalities in common use. Chapter 3: We prove the existence of global solutions and global attractors for thermoelastic coupled beam equations with two memory terms. Chapter 4: We prove the global attraction of thermoelastic coupled beam equations with memory terms and strong damping terms. The existence of children.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.2
本文编号：2210310
[Abstract]:Thermoelastic coupling beam equation is a mathematical model based on the law of deformation and temperature distribution of the beam. This kind of model permeates every field of natural science and has practical research background. This paper mainly discusses the existence of global attractor for non-autonomous thermoelastic coupling beam, including the equations of thermoelastic coupling beam with two memory terms. The initial-boundary value problem and the initial-boundary value problem for a thermoelastic coupled beam system with memory term and strong damping term are first transformed into an autonomous system. The well-posedness theorem of the solution is proved by using semigroup theory. Then the existence of bounded absorption sets for the corresponding infinite-dimensional dynamical systems is proved by using classical integral estimation method. By using the classical integral estimation method, the asymptotic compactness of the solution semigroup of the system is proved, and the existence of the global attractor of the system is obtained. The basic knowledge used includes basic space, lemma, concepts, assumptions and some inequalities in common use. Chapter 3: We prove the existence of global solutions and global attractors for thermoelastic coupled beam equations with two memory terms. Chapter 4: We prove the global attraction of thermoelastic coupled beam equations with memory terms and strong damping terms. The existence of children.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.2
【参考文献】
相关期刊论文 前2条
1 王旦霞;张建文;张建国;;具有结构阻尼和外阻尼的非自治非线性梁方程的拉回D_δ,E_1-吸引子[J];数学的实践与认识;2012年11期
2 PARK Jong Yeoul;KANG Jum Ran;;Global attractor for hyperbolic equation with nonlinear damping and linear memory[J];Science China(Mathematics);2010年06期
相关硕士学位论文 前1条
1 班爱玲;具有临界增长指数的阻尼波动方程的吸引子和核截面的维数[D];上海师范大学;2009年
，本文编号：2210310
本文链接：https://www.wllwen.com/shoufeilunwen/benkebiyelunwen/2210310.html
