耗散camassa-holm方程的cauchy问题及数值分析.doc
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耗散camassa-holm方程的cauchy问题及数值分析,耗散camassa-holm方程的cauchy问题及数值分析目录第一章 序言11.1 camassa-holm方程的物理背景11.2camassa-holm方程的研究现状2第二章 一个弱耗散camassa-holm方程的cauchy问题32.1 引言32.2 局部适定性32.3 解的爆破与爆破率5第三章 经典camas...
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耗散Camassa-Holm方程的Cauchy问题及数值分析
目录
第一章 序言 1
1.1 Camassa-Holm方程的物理背景 1
1.2 Camassa-Holm方程的研究现状 2
第二章 一个弱耗散Camassa-Holm方程的Cauchy问题 3
2.1 引言 3
2.2 局部适定性 3
2.3 解的爆破与爆破率 5
第三章 经典Camassa-Holm方程的数值计算 8
3.1 前言 8
3.2差分格式的构造 9
3.3差分格式的截断误差 10
3.4 差分格式的稳定性及收敛性分析 12
3.5 本章小结 13
结论 14
致谢 15
参考文献 16
摘要：本文主要针对Camassa-Holm方程，关于一类带有耗散项的CH方程的Canchy问题进行理论分析，并对经典的CH方程进行数值分析。
第一章中，简略的介绍了Camassa-Holm方程的物理背景，然后对其研究的现状进行了基本的了解。
第二章，对于特定的一类带有耗散项的CH方程， 关于它的Cauchy问题，我们给出其局部适应性的条件。在此条件下，得出有限时间内发生爆破的充要条件和具体的爆破率，得出尽管耗散程度的强弱明显对方程解的爆破产生影响，但是对于爆破率没有影响。
第三章中，给出了方程具体的求解过程，其相当复杂，所以就Camassa-Holm方程，采用差分法进行近似，并对差分格式的稳定性和收敛性进行了分析，得到 在截断误差范围内，给出的格式是稳定的，且截断误差相容，格式收敛。
关键字：Camassa-Holm方程 全局适定性 爆破与爆破率 数值分析
The Cauchy problem and numerical analysis to the Dissipative Camassa - Holm equation
Abstract
This article mainly aims at Camassa - Holm equation about CH equation with dissipative term Canchy problem of theoretical analysis, and numerical analysis was carried out on the classical equation of CH.
The first chapter briefly introduces the Camassa - Holm equation, the physical background and the present conditions of research on its basic level of understanding.
The second chapter, for a particular kind of CH equation with dissipative term, we give the conditions of local adaptation. Under this condition, it is concluded that the limited time, necessary and sufficient condition of blasting and the blasting rate, it is concluded that although the strength of the degree of dissipation significantly affect equations of blasting, but has no effect for blasting rate.
In the third chapter, we give the solution of the equation of the specific process, its quite complicated, so Camassa - Holm equation, the finite difference method is adopted to improve the approximation, and the stability and convergence of difference scheme are analyzed, and be within the scope of the truncation error, the given format is stable, and the truncation error, format of convergence.
Keywords: Camassa - Holm equation The global well-posedness
The rate of blasting and blasting Numerical analysis
目录
第一章 序言 1
1.1 Camassa-Holm方程的物理背景 1
1.2 Camassa-Holm方程的研究现状 2
第二章 一个弱耗散Camassa-Holm方程的Cauchy问题 3
2.1 引言 3
2.2 局部适定性 3
2.3 解的爆破与爆破率 5
第三章 经典Camassa-Holm方程的数值计算 8
3.1 前言 8
3.2差分格式的构造 9
3.3差分格式的截断误差 10
3.4 差分格式的稳定性及收敛性分析 12
3.5 本章小结 13
结论 14
致谢 15
参考文献 16
摘要：本文主要针对Camassa-Holm方程，关于一类带有耗散项的CH方程的Canchy问题进行理论分析，并对经典的CH方程进行数值分析。
第一章中，简略的介绍了Camassa-Holm方程的物理背景，然后对其研究的现状进行了基本的了解。
第二章，对于特定的一类带有耗散项的CH方程， 关于它的Cauchy问题，我们给出其局部适应性的条件。在此条件下，得出有限时间内发生爆破的充要条件和具体的爆破率，得出尽管耗散程度的强弱明显对方程解的爆破产生影响，但是对于爆破率没有影响。
第三章中，给出了方程具体的求解过程，其相当复杂，所以就Camassa-Holm方程，采用差分法进行近似，并对差分格式的稳定性和收敛性进行了分析，得到 在截断误差范围内，给出的格式是稳定的，且截断误差相容，格式收敛。
关键字：Camassa-Holm方程 全局适定性 爆破与爆破率 数值分析
The Cauchy problem and numerical analysis to the Dissipative Camassa - Holm equation
Abstract
This article mainly aims at Camassa - Holm equation about CH equation with dissipative term Canchy problem of theoretical analysis, and numerical analysis was carried out on the classical equation of CH.
The first chapter briefly introduces the Camassa - Holm equation, the physical background and the present conditions of research on its basic level of understanding.
The second chapter, for a particular kind of CH equation with dissipative term, we give the conditions of local adaptation. Under this condition, it is concluded that the limited time, necessary and sufficient condition of blasting and the blasting rate, it is concluded that although the strength of the degree of dissipation significantly affect equations of blasting, but has no effect for blasting rate.
In the third chapter, we give the solution of the equation of the specific process, its quite complicated, so Camassa - Holm equation, the finite difference method is adopted to improve the approximation, and the stability and convergence of difference scheme are analyzed, and be within the scope of the truncation error, the given format is stable, and the truncation error, format of convergence.
Keywords: Camassa - Holm equation The global well-posedness
The rate of blasting and blasting Numerical analysis
