課程大綱及進度表
開課系所 數學系 開課學年 101 學年度 開課學期 上學期
課程名稱(中文) 雙曲偏微分方程
課程名稱（英文） Hyperbolic Partial Differential Equations 課程碼 L166800
分班碼 星期四 09:10 ~ 12:00 (3177)
先修科目或先備能力 高等微積分，微分方程和偏微分方程（一）
學分數 3 開課教師 方永富
e-mail fang@math.ncku.edu.tw 電話 275-7575 轉 65131
Office Hours Mon and Thu : 12:10 - 13:00, and plus appointments
課程概述 We study the concepts and hyperbolic types of PDE, and their properties, including the geometry of Minkowski spacetime. Then we discuss the fundamental solutions for Klein-Gordon equation, for Dirac equation, for Schr\”odinger equation, and for wave equation. Next we investigate the low regularity global well-possedness for the Zakharov system and for Dirac-Klein-Gordon equations. Finally we consider the scattering problem for the cubic nonlinear Klein-Gordon equation and for the Dirac-Klein-Gordon equations.
教學目標 We expect students to grab the basic idea and concept of PDE. Then we learn various properties of important types of PDE from different aspects. We focus on the wave type equations and emphasize the geometry depicted in the equations, i.e. the geometry of Minkowski spacetime. We expect students to learn the regulairy problem and scattering problem for the equations.
授課課程大綱明細
Ch01: Geometry of Minkowski Spacetime
Ch02: Long Range Scattering for the Nonlinear Klein-Gordon Equation
Ch03: Asymptotic Completeness for the Critical Nonlinear Klein-Gordon Equation Ch04: Low Regularity Global Well-posedness for the Zahkarov System
Ch05: Low Regularity Global Well-posedness for the Klein-Gordon-Schr\”odinger System Ch06: Bilinear Local Smoothinng Estimate for Airy Equation
Ch07: Global solutions for the Dirac-Klein-Gordon system in two space dimensions
參考書目 Partial Differential Equations, An Introduction ( Chapter 1 - 12) by Walter Strauss Lectures On Nonlinear Hyperbolic Differential Equations by Lars H\”ormander Harmonic Analysis by E. M. Stein
課程要求 Advanced Calculus, Differential Equations, and PDE (I)
評量方式 Homework: 40% Presentation: 60%
缺席扣分原則：缺席一堂課扣學期成績一分 課程網址 http://www.math.ncku.edu.tw/~fang 助教資訊
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