Theory of Partial Differential Equations

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Page iii

Copyright page
Page iv

Preface
Pages xi-xiv

Part I An Outline
Page 1

Chapter 1 The Theory of Characteristics, Classification, and the Wave Equation in E2
Pages 3-28

Chapter 2 Various Boundary-Value Problems for the Homogeneous Wave Equation in E2
Pages 29-44

Chapter 3 Various Boundary-Value Problems for the Laplace Equation in E2
Pages 45-58

Chapter 4 Various Boundary-Value Problems for Simple Equations of Parabolic Type
Pages 59-72

Chapter 5 Expectations for Well-Posed Problems
Pages 73-95

Part II Some Classical Results for Nonlinear Equations in Two Independent Variables
Pages 97-99

Chapter 6 Existence and Uniqueness Considerations for the Nonhomogeneous Wave Equation in E2
Pages 101-117

Chapter 7 The Riemann Method
Pages 118-130

Chapter 8 Classical Transmission Line Theory
Pages 131-141

Chapter 9 The Cauchy-Kovalevski Theorem
Pages 142-155

Part III Some Classical Results for the Laplace and Wave Equations in Higher-Dimensional Space
Page 157

Chapter 10 A Sketch of Potential Theory
Pages 159-176

Chapter 11 Solution of the Cauchy Problem for the Wave Equation in Terms of Retarded Potentials
Pages 177-197

Part IV Boundary-Value Problems for Equations of Elliptic-Parabolic Type
Pages 199-200

Chapter 12 A Priori Inequalities
Pages 201-214

Chapter 13 Uniqueness of Regular Solutions and Error Bounds in Numerical Approximation
Pages 215-220

Chapter 14 Some Functional Analysis
Pages 221-239

Chapter 15 Existence of ℒP-Weak Solutions
Pages 240-252

Notes
Pages 253-263

References
Pages 264-266

Index
Pages 267-283