Camassa-Holm方程论文：Camassa-Holm方程动量密度支集特征值广义Camassa-Holm方程

1、Camassa-Holm 方程论文：Camassa-Holm 方程动量密度支集特征值广义 Camassa-Holm 方程【中文摘要】本文首先考虑的是全空间上 camass-HoImfc 皿方程 解的动量密度紧支集长度的估限，方法是运用区间长度与区间特征值 的关系，通过估汁 Dirichlet拉普拉斯算子的特征值来估汁动量密度紧支集的长度接着考虑了在半轴上 cII 方程解的动量密度紧支集大 小的估计，得到与全轴上相同的结论最后，把该动最密度的估计推广 到一类广义Canassa-Holm 方程中，得到与 CH 方陧相似的结论文献巾 已知有紧义集的动最密度以后部有紧支集，本文的估计为这个现象提 供更

2、详细的描述，又已知动最密度紧支集外解的性态，所以估计支集的大小就是估计解不太清楚的区域的大小，加深我们对解的理解本文 共分五章第一章给出本文要考虑的问题和研究肯景，并给出主要定理第二章给出本文中所要用到的记号、 公式以及主要结论第三章给出厶 文主要定理的征明，即存全空间上 cH 方程解的动量密度的紧支集的 估，第四章考虑存半轴上 cH 方程解的动量密度的紧支集的估计第五 章把第三章的结沦，推广到一类广义Camassa-Holm 方程第穴章为总结和指出以后还可以继续研究的问题【英文摘要】In this paper, firstly, we consider the bounds for thes

3、ize of the supportof a compactly supported mome ntum den sity of theCamassa-Holmequatio n on the whole line. This is achieved by estimating the eige nvalue of theDirichletLaplacianoperator, exploitingthe relationsbetweenthe eige nv alues and the ge-ometric properties of a doma in.Secon dly, we con s

4、ider the bounds for the size ofthe compactlysupported mome ntum den sity of the Camassa-Holmequati on on thehalf-line,Wecan get the same conclusion as above. Lastly, weexte nd theestimate of the size of the compactly supported mome ntumden sity to a type ofge neralized Camassa-Holm equati ont is kno

5、wn thatcompactly support mome ntum den sity will remain com-pactly support.The estimate of the size of the support in this thesis furtherelaborates thisresult. Also the behavior of the soluti on outside the support ofthe momentum density is known. Hence we are estimating the size of the regionoverwh

6、ich the solution is not that well understood.This paper is divided intofive sections. In the Section 1, we give the back-ground of the topic we arestudying and state the main theorems. In section 2,we give the notation,and thepreliminaries to be used in the paper.In section 3,we prove the maintheore

7、m, giving an estimate of the size of the support of acompactlysupported mome ntum den sity of the Camassa-Holm equati on onthewhole line. In secti on 4, the same problem on the half-li ne is considered. In secti on 5, we exte nd the con clusi on of secti on 3 to a type ofgen eralized Camassa-Holm40e

8、quati on. In secti on 6, we do a summary and point out some problemstobe studied.【关键词】Camassa-Holm 方程动量密度支集特征值广义Camassa-Holm 方程【英文关键词】Camassa-Holm equati onMome ntumden sitySupportEige nv alueGen eralizedCamassa-Holm equati on【目录】Camassa-Holm 方程解的动量密度紧支集的估计摘要5-6 Abstract 6 第一章 引言 8-131.1 研究的问题81.2 天于（Camassa-Holm 方程的由来和研究背景 8-101.3本文的工作 10-13 第二章 预备知识 13-19 第三章 全空间上 CH 方程解的动量密度紧支集估计19-25 第四章半轴上 CH 方程解的勐量密度紧支集的估计 25-30 第五章一类广义 CH 方程解的动 量密度紧支集的估计30-34 第六章总结与展望34-35