發(fā)布時間：2018-08-28 19:00

【摘要】：熱彈耦合梁方程是根據(jù)梁的變形規(guī)律以及溫度分布規(guī)律建立的數(shù)學模型,這類模型滲透在自然科學的各個領(lǐng)域,有實際的研究背景.本文主要探究了非自治熱彈耦合梁整體吸引子存在性問題,包括具有雙記憶項的熱彈耦合梁方程組的初邊值問題以及具有記憶項和強阻尼項的熱彈耦合梁方程組的初邊值問題,首先將非自治系統(tǒng)轉(zhuǎn)化為自治系統(tǒng),應(yīng)用半群理論證明了解的適定性定理,其次利用經(jīng)典積分估計方法證明系統(tǒng)對應(yīng)的無窮維動力系統(tǒng)存在有界吸收集,最后利用經(jīng)典積分估計方法方法證明系統(tǒng)對應(yīng)的解半群的漸近緊性,進而得到系統(tǒng)整體吸引子的存在性.全文結(jié)構(gòu)如下:第一章:簡要介紹了熱彈耦合梁方程組的研究背景和現(xiàn)狀,同時概述了本文的主要工作和主要結(jié)果.第二章:介紹了本文用到的基礎(chǔ)知識,包括基本空間、引理、概念、假設(shè)以及一些常用的不等式.第三章:證明了具有雙記憶項的熱彈耦合梁方程組整體解的存在性以及整體吸引子的存在性.第四章:證明了具有記憶項和強阻尼項的熱彈耦合梁方程組整體吸引子的存在性。
[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.
【學位授予單位】：太原理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175.2

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本文編號：2210310