北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > Hyperbolic Systems of First-order Equations \(ICBS\)
Hyperbolic Systems of First-order Equations
Aim of this course is to provide a comprehensive introduction to the theory and applications of hyperbolic partial differential equations (PDEs), a fundamental class of equations that describe wave propagation, conservation laws, and various physical phenomena. The course begins by introducing the basic concepts and characteristics of hyperbolic PDEs, including well-posedness, existence, uniqueness, and stability of solutions. We will explore both linear and nonlinear systems, focusing on canonical examples such as the wave equation, transport equations, and systems of conservation laws.

Key topics include the method of characteristics, Riemann invariants, shock waves, and rarefaction waves. The course will also delve into numerical methods for solving hyperbolic systems, discussing finite difference schemes, and addressing the challenges of capturing discontinuities and shocks. Applications in fluid dynamics, traffic flow, and other areas will be examined to highlight the relevance and utility of hyperbolic PDEs in modeling real-world problems.
Professor Lars Aake Andersson
讲师
马志婷
日期
2024年10月08日 至 12月24日
位置
Weekday Time Venue Online ID Password
周二 13:30 - 16:55 A3-4-312 ZOOM 02 518 868 7656 BIMSA
参考资料
1."Partial Differential Equations, Vol. 3: Nonlinear Equations" by L. C. Evans
2."Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves" by Peter D. Lax
3."Introduction to the Theory of Linear Partial Differential Equations" by J. Chazarain and A. Piriou
4."Hyperbolic Differential Operators and Related Pseudodifferential Operators" by Lars Hörmander
5."Linear and Quasi-linear Equations of Hyperbolic Type" by Olga A. Ladyzhenskaya
6."Shock Waves and Reaction-Diffusion Equations" by Joel Smoller
听众
Undergraduate , Advanced Undergraduate , Graduate , 博士后 , Researcher
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
Zhiting Ma obtained the B.S. degree from Lanzhou University in 2015 and Ph.D. degree from Department of Mathematical Sciences at Tsinghua University, China in 2021. Then, she worked as a postdoc at School of Mathematical Sciences, Peking University. Currently, she is an Assistant Professor in Beijing Institute of Mathematical Sciences and Applications (BIMSA). Her current research interests include kinetic theory, machine learning and hyperbolic relaxation systems.
北京雁栖湖应用数学研究院
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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