簡易檢索 / 詳目顯示

研究生: 李正一
Lee, Cheng-I
論文名稱: DKG系統的解在1+3維的存在性
The Existence Of Solution About Dirac-Klein-Gordon System In 1+3 Dimentions
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: 2009
畢業學年度: 97
語文別: 英文
論文頁數: 35
中文關鍵詞: DKG系統
外文關鍵詞: DKG
相關次數: 點閱:64下載:2
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • DKG系統在限制的時間與特殊的空間之下,我們可以透過疊代法以及一些不等式的運算去證明出解在1+3維的存在性與唯一性。

    If the DKG system restricted by time and special space, then we can prove that the solution of DKG system will have existence and uniqueness.

    Contents 1 INTRODUCTION 2 2 PRELIMINARIES 4 3 SOME PROPERTIES OF Xs;b AND Hs;b 7 4 PROOF OF THEOREM 1

    References
    [Bo] N. Bournaveas, Low regularity solutions of the Dirac-Klein-Gordon equations in two space dimensions. Comm. Partial Differential Equations 26,1345-1366 (2001)
    [Ch] J. M. Chadam, Global solutions of the Cauchy problem for the (classical)coupled Maxwell-Dirac equations in one space dimension. J. Funct. Anal.13, 173-184 (1973)
    [B] J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I, II. Geom.Funct. Anal. 3, 107-156 and 209-262(1993)
    [Ke] C. Kenig, G. Ponce, L. Vega, The Cauchy problem for the KdV equation in Sobolev spaces of negative indices. Duke Math. J. 71, 1-21 (1993)
    [K1] S. Klainerman, M. Machedon, Smoothing estimates for null forms and applications. Duke Math. J. 81, 99-133 (1995)
    [K2] S. Klainerman, S. Selberg, Bilinear estimates and applications to nonlinear wave equations. Commun. Contemp. Math. 4, 223-295 (2002)
    [S1] S. Selberg, Multilinear spacetime estimates and applications to local existence theory for nonlinear wave equations. Ph.D. thesis, Princeton Univ.(1999)
    [S2] S. Selberg, On an estimate for the wave equation and applications to nonlinear problems. Di®erential Integral Equations 2, 213-236 (2002)
    [K3] S. Klainerman, M. Machedon, Space-time estimates for null forms and the local existence theorem. Comm. Pure Appl. Math. 46, 1221-1268(1993)
    [St] R. Strichartz, Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44, 705-714 (1977)
    [Ss] P. D'ancona, D. Foschi, S. Selberg, Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system
    [F1] Y. F. Fang, On the Dirac-Klein-Gordon equations in one space dimension. Differential Integral Equations 17, 1321-1346 (2004)
    [F2] Y. F. Fang, M. Grillakis, On the Dirac-Klein-Gordon equations in three space dimensions. Comm. Partial Di®erential Equations 30, 783-812(2005)
    [Fo] D. Foschi, S. Klainerman, Bilinear space-time estimates for homogeneous wave equations. Ann. Sci. Ecole Norm. Sup. (4) 23, 211-274 (2000)

    下載圖示
    2009-07-01公開
    QR CODE