非线性粘弹波方程在Rn中解的爆破 Alternative Title Blow up of solutions of a nonlinear viscoelastic wave equation in Rn 钱金菊 Thesis Advisor 宋海涛 2014-05-28 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 粘弹性波方程 爆破 非线性阻尼 强阻尼 初始能量 Abstract 波方程是偏微分方程理论的一个重要的研究内容，对它的研究必将促进偏微分方程理论和其他数学分支的进一步发展。本文利用凸性分析方法和能量函数方法，研究了两个非线性粘弹波方程解的爆破。下面具体介绍本文的研究工作。 首先，我们介绍了有关问题的研究背景与发展概况以及所研究的主要内容和结构。 其次，给出了解决有关问题的预备知识，列出了证明主要结果用到的定理和不等式。 最后，在前人的研究基础上，通过波的有限传播，分别证明了非线性阻尼项粘弹波方程和对此方程进行微小扰动而形成的新方程在无界区域解的爆破。 Other Abstract Wave equation is an important research content of the theory of partial differential equations, the study of it will promote the theory of partial differential equations and the further development of other branches of mathematics. In this paper, by using convex analysis method and energy function method, studied the blow up of the two nonlinear viscoelastic wave equations. The research work of this paper detailed below. 　　Firstly, We introduce the background and overview of issues related to development and the main content and structure of the research . Secondly, given the prior knowledge to solve the problem, a list of theorems and inequalities to prove the main results . The last, on the basis of predecessors’research, though limited transmission of the wave, proves that the non-linear damping viscoelastic wave equation and a tiny disturbance which was added to this equation and the formation of a new equation of solution of blow up in the region of the unbounded , respectively. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225447 Collection 数学与统计学院 Recommended CitationGB/T 7714 钱金菊. 非线性粘弹波方程在Rn中解的爆破[D]. 兰州. 兰州大学,2014.
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