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

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