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研究生: 賴仕峰
Lai, Shih-Feng
論文名稱: 一維空間之 Dirac-Klein-Gordon 方程
On the Dirac-Klein-Gordon Equations in one Space Dimension
指導教授: 方永富
Fang, Yung-fu
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2004
畢業學年度: 92
語文別: 英文
論文頁數: 60
中文關鍵詞: Dirac-Klein-Gordon 方程
外文關鍵詞: Dirac-Klein-Gordon Equation
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      First, we obtain some solutions representations in Fourier transform. Next we demonstrate that a priori estimates of solutions for Dirac equation and for wave equation. Then we prove a local result for (0.1), taking advantage of the null form estimate, other estimates, and a fixed point argument. Finally we show the local and global results.

    0. Introduction and Main Result 1 1. Solution Representation 3 2. Estimates 17 3. Local and Global Existence 29 4. Null Form Estimate 36 References 59

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    [Bo] N.Bournaveas, A new proof of global existence for the Dirac-Klein-Gordon equation in one space dimension, J.Funct. Anal. 173 (2000), 203-213.]

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    [F1] Yung-fu Fang, Local Existence for Semilinear Wave Equations and Applications to Yang-Mills Equations},Ph.D dissertation (1996) (University of Maryland).

    [F2] Yung-fu Fang, Existence and Uniqueness for Dirac-Klein-Gordon Equations in One Space Dimension (2002)(preprint)

    [F3] Yung-fu Fang, A Direct Proof of Global Existence for the Dirac-Klein-Gordon Equations in One Space Dimension (2004) Taiwanese Journal of Math.

    [FG] Yung-fu Fang and Manoussos Grillakis, Existence and Uniqueness for Boussinesq type Equations on a Circle}, Comm. PDE (1996), 1253-1277.

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    [KM] S. Klainerman and M.Machedon, Space-time estimates for null forms and the local existence theorem}, Comm. Pure Appl. Math. XLVI (1993), 1221-1268.

    [KU] Sergej Kuksin, Infinite-Dimensional Symplectic Capacities and a Squeezing Theorem for Hamiltonian PDE's, Commun. Math. Phys 167 (1995), 531-552.

    [S] E.M. Stein, Singular Integrals and Differentiability Properties of Functions (1970), Princeton University Press.

    [Z] Y. Zheng, Reqularity of weak solutions to a two-dimensional modified Dirac-Klein-Gordon system of equations}, Commun. Math. Phys. 151 (1993), 67-87.

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