《非線性雙曲型偏微分方程講義》是2003年Hormander出版社出版的圖書，作者是Hormander王明新。
基本介紹
- 書名：非線性雙曲型偏微分方程講義
- 作者：Hormander 、王明新
- 原版名稱：Lectures on Nonlinear Hyperbolic Differential Equations
- 類別：科技
- 出版社：Hormander
- 出版時間：2003年
內容簡介,目錄,
內容簡介
本書是以作者1986年～1987年在 Lund大學三個學期授課的講義為基礎，經改寫而成的，主要論述了非線性雙曲型偏微分方程解的全局存在性或“爆破”(blowup)，以及解的奇異性傳播。書中所用的方法是基於對波方程或Yang-Mills方程的非線性攝動研究中採用的保角變換，以及對非線性方程解的余法向奇異性的傳播。
目次：常微分方程；一個空間變數的一階標量方程；多個空間變數的一階標量方程；一個空間變數的一階守恆律系統；補償列緊性；波方程的非線性攝動；Klein-Gordon方程的非線性攝動；微局部分析；擬微分運算元；仿微分計算；奇異性的傳播。
讀者對象：本書可作為大學生在學習基礎的分布理論、測度論和泛函分析等課程之後，進一步學習非線性雙曲型偏微分方程的教科書。
目錄
Preface
Contents
Chapter Ⅰ Ordinary differential equations
1.1 Introduction
1.2 Local existence and uniqueness for the Cauchy problem
1.3 Existence of solutions in the large
1.4 Generalized solutions
Chapter Ⅱ Scalar first order equations with one space variable
2.1 Introduction
2.2 The linear case
2.3 Classical solutions of Burges'equation
2.4 Weak solutions of Burgers'equation
2.5 General strictly convex conservation laws
Chapter Ⅲ Scalar first order equations with several variables
3.1 Introduction
3.2 Parabolic equations
3.3 The conservation law with viscosity
3.4 The entropy solution of the conservation law
Chapter Ⅳ First order systems of conservation laws with one space variable
4.1 Introduction
4.2 Generalities on first order systems
4.3 The lifespan of classical solutions
4.4 The Riemann problem
4.5 Glimm's existence theorem
4.6 Entropy pairs
Chapter Ⅴ Compensated compactness
5.1 Introduction
5.2 Weak convergence in Loo
5.3 Weak convergence of solutions of linear differential equations
5.5 Probability measures associated with a system of two equetions
5.6 Existence of weak solutions for a system of two equations
Chapter Ⅵ Nonlinear perturbations of the wave equation
Chapter Ⅶ Nonlinear perturbations of the Klein-Gordon equation
Chapter Ⅷ Microlocal analysis
Chapter Ⅸ Pseudo-differential operators of type1,1
Chapter Ⅹ Paradifferential calculus
Chapter Ⅺ Propagation of singularities
Appendix on pseudo-Riemannian geometry
References
Index of notation
