课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
MAT7069 偏微分方程 (下)
MAT7069 PDE II
2.
课程性质
Compulsory/Elective
选修 elective
3.
课程学分/学时
Course Credit/Hours
3
4.
授课语言
Teaching Language
英文
English
5.
授课教师
Instructor(s)
苏琳琳助理教授
Assistant Prof. Linlin Su
6.
是否面向本科生开放
Open to undergraduates
or not
是 yes
7.
先修要求
Pre-requisites
本科课程：MA303 偏微分方程，MA301 实变函数，MA302 泛函分析
Undergraduate courses: PDE, Real Analysis (Lebesgue theory), Functional
Analysis
8.
教学目标
Course Objectives
（如面向 本 科 生开放， 请 注 明 区 分 内容 。 If the course is open to undergraduates, please indicate the
difference.）
以介绍偏微分方程的基本理论和方法为主并结合该领域的科研前沿介绍一些具有应用背景的例子.
The main part of this course consists the basic theories and methods of partial differential equations. Some
examples with application background from the research frontier in this field will also be introduced.
9.
教学方法
Teaching Methods
（如面向本科生开放，请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.）
以板书教学为主.
Mainly blackboard-chalk teaching.
10.
教学内容
Course Contents
（如面向本科生开放，请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.）
Section 1
A brief introduction to elliptic interior and global regularity theories, the L
p
and Schauder estimates
Section 2
L² theory for 2nd order parabolic equations, existence via Galerkin method,
uniqueness and regularity via energy method
Section 3
L² theory for 2nd order hyperbolic equations, existence via Galerkin method,
uniqueness and regularity via energy method
Section 4
Nonlinear elliptic equations, variational method—the direct minimization
method, method of upper and lower solutions, fixed point method
Section 5
Nonlinear parabolic equations, global existence, stability of steady states,
traveling wave solutions
Section 6
Conservation laws, Rankine-Hugoniot jump condition, uniqueness issue,
vanishing viscosity method, entropy condition, Riemann problem for Burger's
equation
Section 7
Section 8
Section 9
Section 10
…………
11.
课程考核
Course Assessment
（
○
1
考核形式 Form of examination；
○
2
.分数构成 grading policy；
○
3
如面向本科生开放，请注明区分内容。
If the course is open to undergraduates, please indicate the difference.）
The semester grade will be given according to performance in homework (40%), midterm (20%), and the final
exam (40%).
12.
教材及其它参考资料
Textbook and Supplementary Readings
Textbook: Partial Differential Equations, 2nd edition (reprint of 2015), by Lawrence C. Evans.
References:
1. Elliptic and Parabolic Equations, by Wu Zhuoqun, Yin Jinxue and Wang Chunpeng, World Scientific
Publishing Co.
2. Elliptic Partial Differential Equations of second Order, by David Gilbarg and Neil S. Trudinger, Springer.
3. Partial Differential Equations, 2nd edition, by Robert C. McOwen, Prentice-Hall.
4. Maximum Principles in Differential Equations, by Murray H. Protter and Hans F. Weinberger, Springer.
