1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请联
系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
偏微分方程（下）
Partial Differential Equations II
2.
授课院系
Originating Department
数学系
Department of Mathematics
3.
课程编号
Course Code
MAT7024
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
秋季 Fall
7.
授课语言
Teaching Language
英文 English
8.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
他授课教师）
Instructor(s), Affiliation&
Contact
（For team teaching, please list
all instructors）
王学锋、数学系、wangxf@sustc.edu.cn
Xuefeng Wang, Department of Mathematics, wangxf@sustc.edu.cn
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
2
授课方式
Delivery Method
讲授
Lectures
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
11.
学时数
Credit Hours
48
48
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
MA302 泛函分析
MA302 Functional Analysis
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
学生通过本课程的学习将掌握偏微分方程中的基本概念、基本理论以及基本方法。此课将为学生们以后阅读参考文献和开
展相关的科研工作打好基础。
The students will learn fundamental concepts, theories, and methods in partial differential equation and be able to apply them to solve
problems. Students will be well prepared to read more advanced literature and carry out related research in the future.
16.
预达学习成果 Learning Outcomes
将采用传统方式教授此课(版书，课堂讨论，作业，课外答疑，闭卷考试)。本课讲授者长期从事偏微方程的科研，知道什
么是科研中最需要的基础知识。教师将高效地利用有限的课时讲授最重要的内容, 并在适当的时候以授课和作业的形式介
绍科研前沿问题。
The course will be taught in the standard way (“chalk and board”, in-class discussion, homework, office hours, close-book exams).
The instructors are experienced researchers in the field of partial differential equations, hence know what are the most needed in real
research. The instructors will be highly efficient in using the class hours to teach the most important material, and to expose the
students to research problems via lectures and homework.
17.
课程内容及教学日历 （如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明
主讲人）
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
Section 1 L² theory for second order parabolic and hyperbolic equations, existence via Galerkin method, uniqueness and
regularity via energy method.（8H）
Section 2 Semigroup theory applied to second order parabolic and hyperbolic equations. （8H）
Section 3 A brief introduction to elliptic and parabolic regularity theories, the Lp and Schauder estimates. （8H）
Section 4 Nonlinear elliptic equations, variational method—the direct minimization method, method of upper and lower
solutions, fixed point method. （8H）
Section 5 Nonlinear parabolic equations, global existence, stability of steady states, traveling wave solutions. （8H）
Section 6 Conservation laws, Rankine-Hugoniot jump condition, uniqueness issue, vanishing viscosity method, entropy condition,
Riemann problem for Burger's equation, p-systems. （8H）
18.
教材及其它参考资料 Textbook and Supplementary Readings
3
1. Partial Differential Equations, by Lawrence C. Evans, American Mathematical Society.
2. Elliptic and Parabolic Equations, by Wu Zhuoqun,Yin Jinxue and Wang Chunpeng, World Scientific Publishing Co.
3. Elliptic Partial Differential Equations of second Order, by David Gilbarg and Neil S.Trudinger, Springer.
4. Linear and Quasilinear Equations of Parabolic Type, by Q. A. Ladyzenskaja, V. A. Solonnikov and N. N. Uralceva, American
Mathematical Society.
5. Partial Differential Equations, 2nd edition, by R. McOwen, Prentice-Hall
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
课堂表现
Class
Performance
小测验
Quiz
课程项目 Projects
平时作业
Assignments
40
期中考试
Mid-Term Test
20
期末考试
Final Exam
40
期末报告
Final
Presentation
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
B. 二级记分制（通过/不通过） Pass/Fail Grading
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority
