本文選題：粘性波方程 + 非線性��； 參考：《曲阜師范大學(xué)》2017年碩士論文

【摘要】：粘彈性力學(xué)是研究粘彈性材料在荷載作用下應(yīng)力和應(yīng)變所滿足的規(guī)律.粘彈性力學(xué)是物理學(xué)和數(shù)學(xué)的交叉學(xué)科.早期關(guān)于粘彈性體的研究并未引起科學(xué)界與工程界的廣泛注意,發(fā)展比較緩慢.但近四十余年來,粘彈性力學(xué)及其相應(yīng)的數(shù)學(xué)理論得到了快速的發(fā)展.在材料科學(xué)中的數(shù)學(xué)理論這一頗受國際應(yīng)用數(shù)學(xué)界重視的前沿領(lǐng)域中,現(xiàn)已成為十分活躍的研究課題.粘彈性力學(xué)中研究的方程大部分都是偏微分方程.特別地,粘彈性波方程的能量衰減研究引起了學(xué)者們的廣泛關(guān)注.本文主要考察非齊次粘性波動(dòng)方程組解的衰減估計(jì),文章分為兩章:第一章我們考慮下面帶有邊界控制的非線性粘彈性波動(dòng)方程組的定解問題(?)其中μ,λ是拉梅常數(shù),u= (u1,…,un)是一個(gè)向量函數(shù),divu=ux11+ux22+…+uxnn是u的梯度,△=(?)且(?)這里Ω是Rn(n≥ 1)的一個(gè)具有光滑邊界αΩ的有界區(qū)域,r 0且g是定義在R+上的正的遞減函數(shù),Γ :=αΩ,Γ = Γ=Γ0 ∪Γ1, m(Γ0∩Γ1) =0,Γ0,Γ1測度大于零,n是αΩ的單位外法向量.第二章我們考慮下面的具有Dirichlet齊次邊界的非線性粘彈性波動(dòng)方程組的定解問題(?)這里Ω是Rn(n≥ 1)中具有光滑邊界αΩ的一個(gè)有界區(qū)域,r 0且g是定義在R+上的正的遞減函數(shù).我們的目標(biāo)是用迭代法得到解的一般(General)能量衰減率.
[Abstract]:Viscoelastic mechanics is the law of stress and strain of viscoelastic materials under load. Viscoelastic mechanics is an interdisciplinary discipline in physics and mathematics. The early studies on viscoelastic materials have not attracted much attention from scientific and engineering circles, and their development is slow. However, viscoelastic mechanics and its corresponding mathematical theory have developed rapidly in the past forty years. The mathematical theory in material science, which has been paid much attention by the international applied mathematics, has become a very active research topic. Most of the equations studied in viscoelastic mechanics are partial differential equations. In particular, the energy attenuation of viscoelastic wave equations has attracted much attention. In this paper, we mainly study the decay estimation of solutions of nonhomogeneous viscous wave equations. This paper is divided into two chapters: in chapter 1, we consider the problem of determining solutions of nonlinear viscoelastic wave equations with boundary control. Where 渭, 位 is the Ramie constant u = u 1, 鈥，

本文編號(hào)：1795002