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研究生:鄭棠壕
研究生(外文):Tang-hao Cheng
論文名稱:KdVB方程初值問題解的存在理論之研究
論文名稱(外文):EXISTENCE THEORY OF THE INITIAL VALUE PROBLEM FOR THE KdVB EQUATION
指導教授:左太政左太政引用關係
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:26
中文關鍵詞:KdVB方程
外文關鍵詞:KdVBTHE KdVB EQUATION
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In this paper, we study the existence, uniqueness and regularity dependence results which are established for the initial value problem to the KdVB equation,
$$u_t+uu_x-\alpha u_{xx}+u_{xxx}=0.$$
The methods used in this paper is to regularize the KdVB equation by the addition of the linear term $-\epsilon u_{xxt},$ hence the existence and uniqueness theory for the initial value problem will be developed by the BBMB equation. Finally we consider the limit $\epsilon \to 0$ to show the strong convergence to solutions of the initial value problem for the KdVB equation.

In this paper, we study the existence, uniqueness and regularity dependence results which are established for the initial value problem to the KdVB equation,
$$u_t+uu_x-\alpha u_{xx}+u_{xxx}=0.$$
The methods used in this paper is to regularize the KdVB equation by the addition of the linear term $-\epsilon u_{xxt},$ hence the existence and uniqueness theory for the initial value problem will be developed by the BBMB equation. Finally we consider the limit $\epsilon \to 0$ to show the strong convergence to solutions of the initial value problem for the KdVB equation.

1.Introduction 1
2.The relevant function spaces 4
3.The main result 6
4.Convergence 12
5.Appendix 22
Reference 25

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