高阶Camassa-Holm方程解的爆破性研究

发布时间：2018-06-03 12:56

本文选题：高阶Camassa-Holm方程 + 爆破　；参考：《江苏大学》2017年硕士论文

【摘要】：非线性偏微分方程解的爆破性质包括解的爆破准则、爆破速率、爆破点集等,是非线性方程研究的基本问题之一。本文主要研究的是二阶Camassa-Holm方程问题解的相关爆破性质。首先通过一系列的先验估计得到二阶Camassa-Holm方程解的爆破准则和爆破速率,然后利用闭集的相关性质得到爆破点集,最后得到了方程的初值解在满足一定的条件下解的爆破点集和非爆破点集。全文主要内容共分为三部分:第一部分研究了二阶Camassa-Holm方程在初值条件有限的情况下解的爆破准则和爆破速率;第二部分利用闭集的相关性质给出了二阶Camassa-Holm方程的爆破点集;第三部分利用先验估计给出了二阶Camassa-Holm方程的初值条件在R上非负或是不变号的情况下的非爆破点集。
[Abstract]:The blasting properties of the solutions of nonlinear partial differential equations include the blasting criterion of solutions, the blasting rate, the set of blasting points, and so on. It is one of the basic problems in the study of nonlinear equations. In this paper, we mainly study the related blasting properties of the solutions of the second order Camassa-Holm equation problem. First, by a series of priori estimates, the blow-up criterion and blasting rate of the solution of the second order Camassa-Holm equation are obtained, and then the set of blasting points is obtained by using the properties of the closed set. Finally, the burst point set and the non-burst point set of the initial solution of the equation are obtained under certain conditions. The main contents of this paper are divided into three parts: in the first part, the blasting criterion and blasting rate of the solution of the second order Camassa-Holm equation are studied under the condition of limited initial value conditions, the second part gives the blasting point set of the second order Camassa-Holm equation by using the properties of the closed set. In the third part, by using the prior estimator, we give the set of non-burst points under the condition that the initial value condition of the second order Camassa-Holm equation is nonnegative or invariant on R.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【相似文献】