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Umfang: 1 online resource (299 p.)

ISBN: 1-282-29039-8 , 9786612290398 , 0-08-095602-5

Serie: Mathematics in science and engineering ; v. 93

Inhalt: Theory of partial differential equations

Anmerkung: Description based upon print version of record. , Front Cover; Theory of Partial Differential Equations; Copyright Page; Contents; PREFACE; PART I: AN OUTLINE; Chapter 1. The Theory of Characteristics, Classification, and the Wave Equation in E2; 1. D' Alembert Solution of the Cauchy Problem for the Homogeneous Wave Equation in E2; 2. Nomenclature; 3. Theory of Characteristics and Type Classification for Equations in E2; 4. Considerations Special to Nonlinear Cases; 5. Compatibility Relations and the Finite-Difference Method of Characteristics; 6. Systems Larger Than Two by Two; 7. Flow and Transmission Line Equations , Chapter 2. Various Boundary-Value Problems for the Homogeneous Wave Equation in E21. The Cauchy or Initial-Value Problem; 2. The Characteristic Boundary-Value Problem; 3. The Mixed Boundary-Value Problem; 4. The Goursat Problem; 5. The Vibrating String Problem; 6. Uniqueness of the Vibrating String Problem; 7. The Dirichlet Problem for the Wave Equation?; Chapter 3. Various Boundary-Value Problems for the Laplace Equation in E2; 1. The Dirichlet Problem; 2. Relation to Analytic Functions of a Complex Variable; 3. Solution of the Dirichlet Problem on a Circle , 4. Uniqueness for Regular Solutions of the Dirichlet and Neumann Problem on a Rectangle5. Approximation Methods for the Dirichlet Problem in E2; 6. The Cauchy Problem for the Laplace Equation; Chapter 4. Various Boundary-Value Problems for Simple Equations of Parabolic Type; 1. The Slab Problem; 2. An Alternative Proof of Uniqueness; 3. Solution by Separation of Variables; 4. Instability for Negative Times; 5. Cauchy Problem on the Infinite Line; 6. Unique Continuation; 7. Poiseuille Flow; 8. Mean-Square Asymptotic Uniqueness , 9. Solution of a Dirichlet Problem for an Equation of Parabolic TypeChapter 5. Expectations for Well-Posed Problems; 1. Sense of Hadamard; 2. Expectations; 3. Boundary-Value Problems for Equations of Elliptic-Parabolic Type; 4. Existence as the Limit of Regular Solutions; 5. The Impulse Problem as a Prototype of a Solution in Terms of Distributions; 6. The Green Identities; 7. The Generalized Green Identity; 8. Lp-Weak Solutions; 9. Prospectus; 10. The Tricomi Problem; PART II: SOME CLASSICAL RESULTS FOR NONLINEAR EQUATIONS IN TWO INDEPENDENT VARIABLES , Chapter 6. Existence and Uniqueness Considerations for the Nonhomogeneous Wave Equation in E21. Notation; 2. Existence for the Characteristic Problem; 3. Comments on Continuous Dependence and Error Bounds; 4. An Example Where the Theorem as Stated Does Not Apply; 5. A Theorem Using the Lipschitz Condition on a Bounded Region in E5; 6. Existence Theorem for the Cauchy Problem of the Nonhomogeneous (Nonlinear) Wave Equation in E2; Chapter 7. The Riemann Method; 1. Three Forms of the Generalized Green Identity; 2. Riemann's Function , 3. An Integral Representation of the Solution of the Characteristic Boundary-Value Problem , English

Weitere Ausg.: ISBN 0-12-449550-8

Sprache: Englisch