| 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: |
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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.
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)