作者：[美]Lawrence C.Evans
页数：754
出版社：高等教育出版社
出版日期：2017
ISBN：9787040469356
电子书格式：pdf/epub/txt
内容简介
这是当今关于偏微分方程 (PDE) 的最权威教材的第二版。它给出了PDE理论学习中现代技术的总览，特别注重非线性方程。本书内容广泛，阐述清晰，已经是PDE方面经典的研究生教材。
本书特色
此教科书的第二版讲述了PDE多的研究方向，更值得称赞的是，Evans教授花了大量时间和精力来使一本已经十分成功和精彩的书变得更好。无需赘言，我毫无保留热情地给每一个有兴趣研究PDE的人推荐此书。
——Mathematical Reviews
对那些准备做PDE研究的研究生来说，此书是非常宝贵的。我希望能在研究生院使用它。
——MAA Reviews
目录
Preface to second editionPreface to first edition1. Introduction 1.1. Partial differential equations 1.2. Examples 1.2.1. Single partial differential equations 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. ReferencesPART I: REPRESENTATION FORMULAS FOR SOLUTIONS2. Four Important Linear PDE 2.1. Transport equation 2.1.1. Initial-value problem 2.1.2. Nonhomogeneous problem 2.2. Laplace’s equation 2.2.1. Fundamental solution 2.2.2. Mean-value formulas 2.2.3. Properties of harmonic functions 2.2.4. Green’s function 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. References3. 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-Jacobi equations 3.3.1. Calculus of variations, Hamilton’s 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 ……
4. Other Ways to Represent SolutionsPART II: THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS5. Sobolev Spaces6. Second-Order Elliptic Equations7. Linear Evolution EquationsPART III: THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS8. The Calculus of Variations9. Nonvariational Techniques10. Hamilton-Jacobi Equations11. Systems of Conservation Laws12. Nonlinear Wave EquationsAPPENDICESAppendix A: NotationAppendix B: InequalitiesAppendix C: CalculusAppendix D: Functional AnalysisAppendix E: Measure TheoryBibliographyIndex
4. Other Ways to Represent SolutionsPART II: THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS5. Sobolev Spaces6. Second-Order Elliptic Equations7. Linear Evolution EquationsPART III: THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS8. The Calculus of Variations9. Nonvariational Techniques10. Hamilton-Jacobi Equations11. Systems of Conservation Laws12. Nonlinear Wave EquationsAPPENDICESAppendix A: NotationAppendix B: InequalitiesAppendix C: CalculusAppendix D: Functional AnalysisAppendix E: Measure TheoryBibliographyIndex
