耗散camassa-holm方程的cauchy問題及數(shù)值分析.doc
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耗散camassa-holm方程的cauchy問題及數(shù)值分析,耗散camassa-holm方程的cauchy問題及數(shù)值分析目錄第一章 序言11.1 camassa-holm方程的物理背景11.2camassa-holm方程的研究現(xiàn)狀2第二章 一個弱耗散camassa-holm方程的cauchy問題32.1 引言32.2 局部適定性32.3 解的爆破與爆破率5第三章 經(jīng)典camas...
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耗散Camassa-Holm方程的Cauchy問題及數(shù)值分析
目錄
第一章 序言 1
1.1 Camassa-Holm方程的物理背景 1
1.2 Camassa-Holm方程的研究現(xiàn)狀 2
第二章 一個弱耗散Camassa-Holm方程的Cauchy問題 3
2.1 引言 3
2.2 局部適定性 3
2.3 解的爆破與爆破率 5
第三章 經(jīng)典Camassa-Holm方程的數(shù)值計算 8
3.1 前言 8
3.2差分格式的構(gòu)造 9
3.3差分格式的截斷誤差 10
3.4 差分格式的穩(wěn)定性及收斂性分析 12
3.5 本章小結(jié) 13
結(jié)論 14
致謝 15
參考文獻 16
摘要：本文主要針對Camassa-Holm方程，關(guān)于一類帶有耗散項的CH方程的Canchy問題進行理論分析，并對經(jīng)典的CH方程進行數(shù)值分析。
第一章中，簡略的介紹了Camassa-Holm方程的物理背景，然后對其研究的現(xiàn)狀進行了基本的了解。
第二章，對于特定的一類帶有耗散項的CH方程， 關(guān)于它的Cauchy問題，我們給出其局部適應性的條件。在此條件下，得出有限時間內(nèi)發(fā)生爆破的充要條件和具體的爆破率，得出盡管耗散程度的強弱明顯對方程解的爆破產(chǎn)生影響，但是對于爆破率沒有影響。
第三章中，給出了方程具體的求解過程，其相當復雜，所以就Camassa-Holm方程，采用差分法進行近似，并對差分格式的穩(wěn)定性和收斂性進行了分析，得到 在截斷誤差范圍內(nèi)，給出的格式是穩(wěn)定的，且截斷誤差相容，格式收斂。
關(guān)鍵字：Camassa-Holm方程 全局適定性 爆破與爆破率 數(shù)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
目錄
第一章 序言 1
1.1 Camassa-Holm方程的物理背景 1
1.2 Camassa-Holm方程的研究現(xiàn)狀 2
第二章 一個弱耗散Camassa-Holm方程的Cauchy問題 3
2.1 引言 3
2.2 局部適定性 3
2.3 解的爆破與爆破率 5
第三章 經(jīng)典Camassa-Holm方程的數(shù)值計算 8
3.1 前言 8
3.2差分格式的構(gòu)造 9
3.3差分格式的截斷誤差 10
3.4 差分格式的穩(wěn)定性及收斂性分析 12
3.5 本章小結(jié) 13
結(jié)論 14
致謝 15
參考文獻 16
摘要：本文主要針對Camassa-Holm方程，關(guān)于一類帶有耗散項的CH方程的Canchy問題進行理論分析，并對經(jīng)典的CH方程進行數(shù)值分析。
第一章中，簡略的介紹了Camassa-Holm方程的物理背景，然后對其研究的現(xiàn)狀進行了基本的了解。
第二章，對于特定的一類帶有耗散項的CH方程， 關(guān)于它的Cauchy問題，我們給出其局部適應性的條件。在此條件下，得出有限時間內(nèi)發(fā)生爆破的充要條件和具體的爆破率，得出盡管耗散程度的強弱明顯對方程解的爆破產(chǎn)生影響，但是對于爆破率沒有影響。
第三章中，給出了方程具體的求解過程，其相當復雜，所以就Camassa-Holm方程，采用差分法進行近似，并對差分格式的穩(wěn)定性和收斂性進行了分析，得到 在截斷誤差范圍內(nèi)，給出的格式是穩(wěn)定的，且截斷誤差相容，格式收斂。
關(guān)鍵字：Camassa-Holm方程 全局適定性 爆破與爆破率 數(shù)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
