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研究生:盧柏誠
研究生(外文):Lu, Bocheng
論文名稱:矩量空間中之梯度流方程組及其伽瑪收斂性
論文名稱(外文):The System Of Gradient Flows On Metric Spaces And Its Gamma-Convergence
指導教授:張茂盛
指導教授(外文):Chang, Maosheng
口試委員:陳建隆陳俊全錢傳仁
口試委員(外文):Chern, JannlongChen, ChiunchuanChyen, Chuanjen
口試日期:2012-06-21
學位類別:碩士
校院名稱:輔仁大學
系所名稱:數學系研究所
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:2012
畢業學年度:100
語文別:英文
論文頁數:26
外文關鍵詞:Gamma convergenceGamma-convergence of gradient flowsmetric derivativecurve of maximal slopestrong upper gradient
相關次數:
  • 被引用被引用:0
  • 點閱點閱:90
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  • 下載下載:2
  • 收藏至我的研究室書目清單書目收藏:0
在本論文中我們完成下列三項工作:
一. 矩量空間中梯度流系統概念之建立。
二. 解析能量消散速率控制某型態之梯度流系統解的矩量速度。
三. 架構矩量空間中梯度流系統的伽瑪收斂理論。
In this manuscript, we introduce the systems of gradient flows on metric spaces and then we investigate an upper control for one form of velocity of solutions by its dissipation rate of energy functional.
This paper essentially presents the abstract structure of ”Gamma-convergence of gradient flow systems on metric spaces”.
The approach is based on the notion initiated by Sylvia Serfaty.
1 Introduction
2 Preliminaries
3 Main results
[1] L. Ambrosio. Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5)(1995) 191-246.
[2] L. Ambrosio, N. Gigli, and G. Savar´e. Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Z¨urich. Birkh¨auser, 2008.
[3] W. Arendt, C. J. K. Batty, M. Hieber, F. Neubrander. Vector-valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics, vol. 96, Birkh¨auser, Basel 2001.
[4] Philippe Cl´ement. An Introduction to Gradient Flows in Metric Spaces. Lecture Note, June 2009.
[5] M. Degiovanni, A. Marino, and M. Tosques. Evolution equations with lack of convexity. Nonlinear Anal., 9(1985) 1401-1443.
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[8] N. Q. Le. On the convergence of the Ohta-Kawasaki equation to motion by nonlocal Mullins-Sekerka law. SIAM J. Math. Analysis 42 (2010), no.4, 1602-1638.
[9] A. Marino, C. Saccon, and M. Tosques. Curves of maximal slope and parabolic variational inequalities on nonconvex constraints. Ann Scuola Norm. Sup. Pisa Cl. Sci. (4), 16(1989), 281-330.
[10] S. Serfaty. Gamma-convergence of gradient flows on Hilbert and metric spaces and applications. Disc. Cont. Dyn. Systems, A, 31, No 4 (2011), 1427-1451.
[11] E. Sandier and S. Serfaty. Gamma-convergence of gradient flows with applications to Ginzburg-Landau. Comm. Pure Appl. Math, 57,No 12, (2004), 1627-1672.
[12] R.L. Wheeden and A. Zygmund Measure and Integral. (1977).
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