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課程名稱 |
變分法及其在非線性偏微分方程的應用
Variational Methods and their Applications to Nonlinear PDE |
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開課學期 |
104-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
林太家 |
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課號 |
MATH5022 |
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課程識別碼 |
221 U6800 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一8,9(15:30~17:20)星期二9(16:30~17:20) |
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上課地點 |
天數305天數305 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042MATH5022_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
We will introduce variational methods and their applications to nonlinear partial differential equations. The main topics of contents are
1. The Direct Methods in the Calculus of Variations
2. Minimax Methods
3. Limit Cases of the Palais-Smale Condition
4. Ginzburg-Landau equations
5. Other related topics
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課程目標 |
This course is for advanced graduate students or anyone who wishes to acquaint himself/herself with variational methods and their applications to nonlinear partial differential equations (PDEs). Basic knowledge of variational methods will be introduced. Students will be trained to use techniques of nonlinear analysis and solve problems of nonlinear PDEs. Students will also be required to read and present papers for their scores. |
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課程要求 |
Real Analysis and Partial Differential Equations (graduate school) |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
Michael Struwe, Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag 1990. |
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參考書目 |
F. Bethuel, H. Brezis and F. Helein, Ginzburg-Landau Vortices, Birkhauser, 1994. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
上台報告 |
100% |
每位同學尋找自己有興趣且與上課內容相關之論文,經研讀並整理後上台報告。 |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22,2/23 |
Introduction to Calculus of Variations |
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第2週 |
2/29,3/01 |
Direct methods |
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第3週 |
3/07,3/08 |
Direct methods |
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第4週 |
3/14,3/15 |
Direct methods |
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第5週 |
3/21,3/22 |
Minimax methods |
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第6週 |
3/28,3/29 |
Minimax methods |
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第7週 |
4/04,4/05 |
春假 |
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第8週 |
4/11,4/12 |
Minimax methods |
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第9週 |
4/18,4/19 |
Ginzburg-Landau equations |
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第10週 |
4/25,4/26 |
Ginzburg-Landau equations |
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第11週 |
5/02,5/03 |
Ginzburg-Landau equations |
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第12週 |
5/09,5/10 |
Ginzburg-Landau equations |
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第13週 |
5/16,5/17 |
vortex dynamics of Ginzburg-Landau equations |
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第14週 |
5/23,5/24 |
Convexity and Compactness |
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第15週 |
5/30,5/31 |
自主學習週 |
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第16週 |
6/06,6/07 |
Palais-Smale condition |
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第17週 |
6/13,6/14 |
出國開會；6/21, 4:30-6:00PM 上台報告 |
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