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姓名 吳彥霖(Yen-Lin Wu) 查詢紙本館藏 畢業系所 數學系 論文名稱
(On the Positive Solution for Grad-Shafranov Equation)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 在這篇論文中,我們考慮由電漿物理所衍生之Grad-Shafranov 方程式(請參考郝玲妮教授與其博士生傅瑋宗之文章[2]、[3])。利用正規擾動方法,我們觀察此方程(在一維情況下)之正解,對其參數Kappa 之極限行為。此外,我們亦提供一些徑向解的結構,諸如全域存在性、唯一性以及漸進行為。
摘要(英) In this thesis, we consider a new type of Grad-Shafranov equation :
$$displaystyle Delta u=Big(1+frac{cu}{kappa}Big)^{-kappa+frac{1}{2}} $$
arising from the plasma physics (see Ref. cite{HF1} and cite{HF2} by L.-N. Hau and W.-Z. Fu). Using the method of regular perturbation, we investigate the limiting behavior of positive solutions (for 1D case) with respect to the parameter Kappa $kappa$ (as $kappa o infty$). In addition, the global existence, uniqueness and asymptotic behavior of positive radial solutions will be proved as well.
論文目次 1. Introduction -----1
2.Observation for Behavior of the Solutions with respect to k -----4
3. Global Existence, Uniqueness and Asymptotic Behavior of Positive Solutions -----10
4. Conclusion Remark -----19
Reference 20
參考文獻 [1] Z.-Y. Chen, J.-L. Chern and Y.-L. Tang, The structure of radial solutions for elliptic equations arising from the spherical Onsager vortex, Tohoku Math. J.61 (2009), 287-307.
[2] L.-N. Hau and W.-Z. Fu, Phys. Plasmas 12, 070701 (2005).
[3] L.-N. Hau and W.-Z. Fu, Mathematical and physical aspects of Kappa velocity distribution, Phys. Plasmas 14, 110702 (2007).
[4] S.-B. Hsu, Ordinary Differential Equations with Applications, Word Scientific Press (2006).
[5] J.A.Murdock, Perturbation Theory and Methods, John Willy and Sons, Inc. New York (1991).
[6] A. H. Nayfeh, Perturbation Methods, Willey, New York (1973).
指導教授 蕭嘉璋、陳建隆
(Chia-Chang Hsiao、Jann-Long Chern)審核日期 2009-6-30 推文 plurk
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