出版时间:2009-6 出版社:世界图书出版公司 作者:约翰 页数:249
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前言
A considerable amount of new material has been added to this edition.There is an extensive discussion of real analytic functions of several variablesin Chapter 3. This permits estimation of the size of the domain of existencein the Cauchy-Kowalevski theorem. A first application of these estimatesconsists in a rigorous proof of a new version of Holmgren's uniquenesstheorem for linear analytic partial differential equations (only sketched inthe earlier editions). As another application (following Schauder) we give asecond proof for existence of solutions of the initial value problem forsymmetric hyperbolic systems in Chapter 5. Chapter 6 now includes a moredetailed study of the Hilbert spaces with applications to the boundarybehavior of solutions of the Dirichlet problem in higher dimensions. ToChapter 7 there has been added a proof of Widder's theorem on non-negativesolutions of the heat equation. Finally, a new chapter, Chapter 8, containsH. Lewy's construction of a linear differential equation without solutions.There are also more problems, designed, in part, to extend the materialdiscussed in the text. 1 am particularly indebted to my colleague Percy A. Deift of the CourantInstitute of New York University, to Prof. A. Garder of the Southern IllinoisUniversity at Edwardsville, Illinois, and to Dr. George Dassios of theNational Technical University of Athens, Greece, for taking the trouble tocompile lists of errors in the third edition. I hope that these have all beencorrected and not too many new ones added in the present edition.
内容概要
本书是一部非常优秀的介绍偏微分方程的入门书籍,可以作为研究生阶段学习的基石。本书详尽地介绍了偏微分方程理论的重要方面,并从数学分析的角度做了进一步的探讨。本书是第4版,增加了全新的一章讲述无解线性方程的Lewy例子。
作者简介
作者:(德国)约翰(John.F.)
书籍目录
Chapter 1 The Single First-Order Equation 1. Introduction 2. Examples 3. Analytic Solution and Approximation Methods in a Simple Example Problems 4. Quasi-linear Equations 5. The Cauchy Problem for the Quasi-linear Equation 6. Examples Problems 7. The General First-Order Equation for a Function of Two Variables 8. The Cauchy Problem 9. Solutions Generated as Envelopes ProblemsChapter 2 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 1. Characteristics for Linear and Quasi-linear Second-order Equations 2. Propagation of Singularities 3. The Linear Second-Order Equation Problems 4. The One-Dimensional Wave Equation Problems 5. Systems of First-Order Equations 6. A Quasi-linear System and Simple Waves ProblemChapter 3 Characteristic Manifolds and the Cauchy Problem 1. Notation of Laurent Schwartz Problems 2. The Cauchy Problem Problems 3. Real Analytic Functions and the Cauchy-Kowalevski Theorem (a) Multiple infinite series Problems (b) Real analytic functions Problems (c) Analytic and real analytic functions Problems (d) The proof of the Cauchy-Kowalevski theorem Problems 4. The Lagrange-Green Identity 5. The Uniqueness Theorem of Holmgren Problems 6. Distribution Solutions ProblemsChapter 4 The Laplace Equation 1. Green's Identity. Fundamental Solutions, and Poisson's Equation Problems 2. The Maximum Principle Problems 3. The Dirichlet Problem, Green's Function, and Poisson's Formula Problems 4. Proof of Existence of Solutions for the Dirichlet Problem Using Subharmonic Functions ("Perron's Method") Problems 5. Solution of the Dirichlet Problem by Hilbert-Space Methods ProblemsChapter 5 Hyperbolic Equations in Higher Dimensions 1. The Wave Equation in n-Dimensional Space (a) The method of spherical means Problems (b) Hadamard's method of descent Problems ……Chapter 6 Higher-Order Elliptic Equations with ConstantChapter 7 Parabolic EquationsChapter 8 H.Lewy's Example of a Linear EquationBibliographyGlossaryIndex
章节摘录
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《偏微分方程(第4版)(英文版)》是由世界图书出版公司出版的。
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