《非线性双曲型偏微分方程讲义》(Lectures on Nonlinear Hyperbolic Differential Equations)英文版[DJVU]_ed2kers电驴资源下载网站

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资源介绍

语言: 英文

地区: 大陆

图书fenlei: 科技

中文名: 非线性双曲型偏微分方程讲义

发行时间: 2003年

原名: Lectures on Nonlinear Hyperbolic Differential Equations

资源格式: DJVU

版本: 英文版

简介:

djvu 阅读器：
http://windjview.sourceforge.net/
内容简介：
本书是以作者1986年～1987年在 Lund大学三个学期授课的讲义为基础，经改写而成的，主要论述了非线性双曲型偏微分方程解的全局存在性或“爆破”(blowup)，以及解的奇异性传播。书中所用的方法是基于对波方程或Yang-Mills方程的非线性摄动研究中采用的保角变换，以及对非线性方程解的余法向奇异性的传播。
目次：常微分方程；一个空间变量的一阶标量方程；多个空间变量的一阶标量方程；一个空间变量的一阶守恒律系统；补偿列紧性；波方程的非线性摄动；Klein-Gordon方程的非线性摄动；微局部分析；拟微分算子；仿微分计算；奇异性的传播。
读者对象：本书可作为大学生在学习基础的分布理论、测度论和泛函分析等课程之后，进一步学习非线性双曲型偏微分方程的教科书。
内容截图：

目录: 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
Index

《非线性双曲型偏微分方程讲义》(Lectures on Nonlinear Hyperbolic Differential Equations)英文版[DJVU]

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