Book:D.L. Colton/Partial Differential Equations in the Complex Domain

D.L. Colton: Partial Differential Equations in the Complex Domain

Published $\text {1976}$, Pitman Publishing

ISBN 0 273 00101 9

Subject Matter

• Partial Differential Equations

Contents

INTRODUCTION

CHAPTER I. PRELIMINARY RESULTS

1. Fundamental Solutions and Analyticity

2. Existence and Uniqueness of Solutions to the Dirichlet and Cauchy Problems

CHAPTER II. IMPROPERLY POSED INITIAL VALUE PROBLEMS

3. Cauchy's Problem in Two Independent Variables

4. Cauchy's Problem for Quasilinear Systems

5. Uniqueness of Solutions to Cauchy's Problem and the Runge Approximation Property

6. The Non-Characteristic Cauchy Problem for Parabolic Equations

7. Improperly Posed Initial-Value Problems for Hyperbolic Equations

CHAPTER III. INTEGRAL OPERATORS FOR ELLIPTIC EQUATIONS

8. Integral Operators in Two Independent Variables

9. Integral Operators for Self Adjoint Equations in Three Independent Variables

10. Integral Operators for Non Self Adjoint Equations in Three Independent Variables

CHAPTER IV. ANALYTIC CONTINUATION

11. Lewy's Reflection Principle and Vekua's Integral Operators

12. The Envelope Method and Analytic Continuation

13. The Axially Symmetric Helmholtz Equation

14. Analytic Continuation of Solutions to the Axially Symmetric Helmholtz Equation

CHAPTER V. PSEUDOPARABOLIC EQUATIONS

15. Pseudoparabolic Equations in One Space Variable

16. Pseudoparabolic Equations in Two Space Variables

REFERENCES