中国伊朗编
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作者(美)劳费尔 著
出版社百家出版社
ISBN9787547512340
出版时间2017-03
装帧精装
开本16开
定价198元
货号1201492622
上书时间2024-09-30
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作者简介
劳费尔，美籍德国藏学家。曾多次来中国科考。精通汉语、藏语及多种语言，是20世纪西方重要的汉学和东方学家之一。主要作品有《中国和欧洲的鸟形车》、《吐蕃的鸟卜》、《西藏文字的起源》等。
目录
Preface to second edition
Preface to first edition
1.Introduction
1.1.Partial differential equations
1.2.Examples
1.2.1.Single partial differential equatioas
1.2.2.Systems of partial differential equations
1.3.Strategies for studying PDE
1.3.1， Well—posed problems， classical solutions
1.3.2.Weak solutions and regularity
1.3.3， Typical difficulties
1.4.Overview
1.5.Problems
1.6.References
PART Ⅰ： REPRESENTATION FORMULAS FOR SOLUTIONS
2.Four Important Linear PDE
2.1.Transport equation
2.1.1.Initial—value problem
2.1.2.Nonhomogeneous problem
2.2.Laplaces equation
2.2.1.Fundamental solution
2.2.2.Mean—vahle formulas
2.2.3.Properties of harmonic functions
2.2.4.Greens fnnction
2.2.5.Energy methods
2.3.Heat equation
2.3.1.Fundamental solution
2.3.2.Mean—value formula
2.3.3.Properties of solutions
2.3.4.Energy methods
2.4.Wave equation
2.4.1.Solution by spherical means
2.4.2.Nonhomogeneous problem
2.4.3.Energy methods
2.5.Problems
2.6.References
3.Nonlinear First—Order PDE
3.1.Complete integrals， envelopes
3.1.1.Complete integrals
3.1.2.New solutions from envelopes
3.2.Characteristics
3.2.1.Derivation of characteristic ODE
3.2.2.Examples
3.2.3.Boundary conditions
3.2.4.Local solution
3.2.5.Applications
3.3.Introduction to Hamilton Jaeobi equations
3.3.1.Calculus of variations， Hamiltons ODE
3.3.2.Legendre transform， Hopf—Lax formula
3.3.3.Weak solutions， uniqueness
3.4.Introduction to conservation laws
3.4.1.Shocks， entropy condition
3.4.2.Lax Oleinik formula
3.4.3.Weak solutions， uniqueness
3.4.4.Riemanns problem
3.4.5.Long time behavior
3.5.Problems
3.6.References
4.Other Ways to Represent Solutions
4.1.Separation of variables
4.1.1.Examples
4.1.2.Application： Turing instability
4.2.Similarity solutions
4.2.1.Plane and traveling waves， solitons
4.2.2.Similarity under scaling
4.3.Transform methods
4.3.1.Fourier transform
4.3.2.Radon transform
4.3.3.Laplace transform
4.4.Converting nonlinear into linear PDE
4.4.1.Cole—Hopf transfornmation
4.4.2.Potential functions
4.4.3.Hodograph and Legendre transforms
4.5.Asymptotics
4.5.1.Singular perturbations
4.5.2.Laplaces method
4.5.3.Geometric optics， stationary phase
4.5.4.Homogenization
4.6.Power series
4.6.1.Noneharacteristic snrfaces
4.6.2.Real analytic functions
4.6.3.Cauehy—Kovalevskaya Theorem
4.7.Problems
4.8.References
PART Ⅱ： THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS
5.Sobolev Spaces
5.1.Holder spaces
5.2.Sobolev spaces
5.2.1.Weak derivatives
5.2.2.Definition of Sobolev spaces
5.2.3.Elementary properties
5.3.Approximation
5.3.1.Interior approximation by smooth functions
5.3.2.Approximation by smooth functions
5.3.3.Global approximation by smooth functions
5.4.Extensions
5.5.Traces
5.6.Sobolev inequalities
5.6.1.Gagliardo Nirenberg Sobolev inequality
5.6.2.Morreys inequality
5.6.3.General Sobolev inequalities
5.7.Compactness
5.8.Additional topics
5.8.1.Poincares inequalities
5.8.2.Difference quotients
5.8.3.Differentiability a.e
5.8.4.Hardys inequality
5.8.5.Fourier transform methods
5.9.Other spaces of functions
5.9.1.The space H—1
5.9.2.Spaces involving time
5.10.Problems
5.11.References
6.Second—Order Elliptic Equations
6.1.Definitions
6.1.1.Elliptic equations
6.1.2.Weak solutions
6.2.Existence of weak solutions
6.2.1.Lax—Milgram Theorem
6.2.2.Energy estimates
6.2.3.Fredhohn alternative
6.3.Regularity
6.3.1.Interior regularity
6.3.2.Boundary regularity
6.4.Maximum principles
6.4.1.Weak maximum principle
6.4.2.Strong maximum principle
6.4.3.Harnacks inequality
6.5.Eigenvalues and eigenfunctions
6.5.1.Eigenvalues of symmetric elliptic operators
6.5.2.Eigenvalues of nonsymmetric elliptic operators
6.6.Problems
6.7.References
……
7.Linear Evolution Equations
PART Ⅲ： THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
APPENDICES
Bibliography
Index
内容摘要
《中国伊朗编》内容首先是中国和古代西域植物的传播关系，其次是关于中亚纺织品、矿物和汉籍著录的伊朗目前萨珊王朝的官制。
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