雙曲偏微分方程導論課程綱要表科

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雙曲偏微分方程導論課程綱要表

科目名稱雙曲偏微分方程導論

英文科目名稱

Introduction to Hyperbolic PDE

授 課教師蘇萾欽

教學方式 Teaching Method

講授與討論

Lecture and Discussion

教學目標 Objective

In this course, we focus on the investigation of quasilinear hyperbolic systems of conservation laws. Moreover, we take a more practical

approach to these systems by emphasizing how the results are used and how they are applied to real problems.

參考書目 Reference

1. Logan J. D., 2008. An Introduction to

Nonlinear Partial Differential Equations, 2^nd ed., Wiley- Interscience, New York.

2. Smoller, J., 1994. Shock Waves and Reaction- Diffusion Equations, 2^nd ed., Springer-Verlag, New York.

尊重智慧財產權，不得非法影印任何有版權的著作

單元主題 I 內容綱要Outline

Reference An Introduction to Nonlinear Partial Differential Equations

Introduction

◎Classification of PDEs

◎One and Higher dimensions of conservation laws

◎Initial and Boundary Value Problems

◎Waves

First-Order

Equations and

Characteristics

◎Linear and Nonlinear Equations

◎The method of Characteristics

◎Some Models

Weak Solutions to Hyperbolic

Equations

◎Discontinuous Solutions and Jump Conditions

◎Rarefaction Waves and Shocks

◎Weak Solutions

◎Asymptotic Behavior of Shocks

Hyperbolic

◎Shallow-Water Waves

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Systems

◎Gas Dynamics

◎Hyperbolic Systems and Characteristics

◎The Riemann Method

單元主題 II 內容綱要Outline

Reference Shock Waves and Reaction-Diffusion Equations

The Riemann

Problem for Systems of

Conservation Laws

◎The p-System

◎Shocks and Simple Waves

◎Solution of the General Riemann Problem

The Glimm Difference

Scheme

◎The Interaction Estimate

◎The Difference Approximation

◎Convergence 評量方式

Evaluation

Home Work and Final Exam

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雙曲偏微分方程導論課程綱要表 科