擬線性波方程中片段線性初始值問題的整體Lipchitz連續解的

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姓名

王世杰(Shih-Chieh Wang) 查詢紙本館藏

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數學系

論文名稱

擬線性波方程中片段線性初始值問題的整體Lipchitz連續解的
(The Global Lipchitz Continuous Solutions to the Quasilinear Wave Equation with Peicewise Linear Initial Data)

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摘要(中)

在這篇論文裡面我們主要是對一些擬線性波方程研究Lipchitz連續解的總體存在性，藉著一次微分的假設當做新的未知數，我們重新把方程式寫成守衡律中的三乘三Hyberlbolic system，這個初始值問題對線性的初始值而言已經被解決了，解的一次微分的整體存在性是藉著Lex method 來建立的。

摘要(英)

In this paper we study the global existence of Lipchitz continous solutions to the quasilinear wave equation. By letting the first derivatives as new unknowns, we rewrite the equation into a 3 by 3 hyperbolicsystem of conservation laws. The initial value problem of the ststem is studied for some linear initial data. The global existence of the first derivatives of solutions are established by Lex method.

關鍵字(中)

★ 擬線性波方程
★ 守恆律
★ 非線性平衡律
★ 黎曼問題
★ Lex方法

關鍵字(英)

★ Lax method
★ Riemann problems
★ Nonlinear balance laws
★ Quasilinear wave equations
★ Conservation laws

論文目次

中文摘要………………………………………………………………i
英文摘要………………………………………………………………ii
圖目錄…………………………………………………………………iii
一. Introduction…………………………………………………….2
二. Elementary Waves and Corresponding Wave Curves…………..5
三. Existence of Weak Solutions, Lipchitz Continuoous Solutions…25
四. Reference…………………………………………………………27

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指導教授

洪盟凱(John M. Hong)

審核日期

2007-11-22

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