本文關(guān)鍵詞：幾類熱彈耦合梁方程組整體解和全局吸引子的研究　出處：《太原理工大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 熱彈耦合梁方程組 非齊次邊界條件 整體解 全局吸引子

【摘要】：本文研究了在Fourier熱傳導(dǎo)定律或Gurtin-Pipkin熱傳導(dǎo)定律下幾類熱彈耦合梁方程組系統(tǒng).考慮了齊次邊界條件和非齊次邊界條件及初始條件下各類系統(tǒng)整體解的存在唯一性和齊次邊界條件及初始條件下系統(tǒng)的全局吸引子的存在性.具體研究內(nèi)容如下：第一章簡要介紹了國內(nèi)外關(guān)于梁方程組系統(tǒng)的研究狀況,同時概述了本文所研究的主要內(nèi)容.第二章給出了本文所用的基本概念、基本引理及一些常用的不等式.第三章運用Faedo-Galerkin方法,結(jié)合先驗估計及一些不等式技巧,研究了Fourier熱傳導(dǎo)定律下具有轉(zhuǎn)動慣量和結(jié)構(gòu)阻尼及非線性外阻尼的非自治熱彈耦合梁方程組在齊次邊界條件u=△u=θ=0 x∈(?)Ω,t∈Rτ,t≥τ和初始條件下系統(tǒng)的整體解的存在唯一性及解對初值的連續(xù)依賴性,其中Ω(?)Rn是Rn中具有充分光滑邊界的有界區(qū)域,且0ω1,υ0.第四章研究了在熱傳導(dǎo)定律下具有非線性外阻尼的熱彈Gurtin-Pipkin耦合梁方程組在非線性邊界條件和初值條件u(x,0)=u0(x),ut(x,0)=u1(x),θ(x,0)=θ0(x)x∈(0,l)下的初邊值問題.第五章討論了具有熱記憶項的可伸梁方程組的長時間動力學(xué)行為.首先運用算子半群方法,結(jié)合Sobolev空間理論及不等式技巧,證明了系統(tǒng)整體解的存在唯一性；其次,基于上述整體解的存在唯一性定義了((?),S(t))動力系統(tǒng),通過先驗估計和一些不等式技巧證明了系統(tǒng)吸收集的存在性,從而得出系統(tǒng)具有耗散性；最后通過構(gòu)造一系列Lyapunov函數(shù)證明了系統(tǒng)是漸近緊的,驗證了具有熱記憶的可伸梁方程在齊次邊界條件及一定初始條件下系統(tǒng)的全局吸引子的存在性.
[Abstract]:In this paper, we study some systems of thermoelastic coupled beam equations under the Fourier's law of heat conduction or Gurtin-Pipkin 's law of heat conduction. We consider the homogeneous boundary condition, the nonhomogeneous boundary condition and the initial condition. The existence and uniqueness of global solutions and the existence of global attractors under homogeneous boundary conditions and initial conditions are discussed in this paper. The first chapter briefly introduces the research status of beam equations system at home and abroad. At the same time, the main contents of this paper are summarized. In chapter two, the basic concepts, basic Lemma and some commonly used inequalities are given. In chapter 3, the Faedo-Galerkin method is used. Combining with a priori estimate and some inequality techniques. In this paper, the nonautonomous thermoelastic coupled beam equations with rotational inertia, structural damping and nonlinear external damping under Fourier's law of heat conduction are studied under homogeneous boundary conditions u = u = 胃 0 x 鈭，

本文編號：1376206