Lectures on Cauchy's Problem in Linear Partial Differential Equations
作者： Hadamard
出版社：高等教育出版社
- 高等教育出版社
- 9787040448047
- 1版
- 47266374-9
- 16开
- 490
- 理学
- 数学类
- 数学类
- 研究生及以上
这些讲义是一个开创性的研究。 基于Riemann, Kirchhoff和Volterra的研究，运用其关于所有正常的双曲型方程组的球面和柱面波的相关理论，阿达马扩展和改进了Volterra的工作。主题包括柯西问题的一般性质，基本公式和基本解，具有奇数独立变量的方程和具有偶数独立变量的方程。
Front Matter
BOOK I. GENERAL PROPERTIES OF CAUCHY’S PROBLEM
I. CAUCHY’S FUNDAMENTAL THEOREM CHARACTERISTICS
II. DISCUSSION OF CAUCHY’S RESULT
BOOK II. THE FUNDAMENTAL FORMULA AND THE ELEMENTARY SOLUTION
I. CLASSIC CASES AND RESULTS
II. THE FUNDAMENTAL FORMULA
III. THE ELEMENTARY SOLUTION
1. General Remarks
2. Solutions with an Algebroid Singularity
3. The Case of the Characteristic e Elementary Solution
Additional Note on the Equations of Geodesics
BOOK III. THE EQUATIONS WITH AN ODD NUMBER OF INDEPENDENT VARIABLES
I. INTRODUCTION OF A NEW KIND OF IMPROPER INTEGRAL
1. Discussion of Preceding Results
2. The Finite Part of an Infinite Simple Integral
3. The Case of Multiple Integrals
4. Some Important Examples
II. THE INTEGRATION FOR AN ODD NUMBER OF INDEPENDENT VARIABLES
III. SYNTHESIS OF THE SOLUTION OBTAINED
IV. APPLICATIONS TO FAMILIAR EQUATIONS
BOOK IV. THE EQUATIONS WITH AN EVEN NUMBER OF INDEPENDENT VARIABLES AND THE METHOD OF DESCENT
I. INTEGRATION OF THE EQUATION IN 2m1 VARIABLES
1. General Formulæ
2. Familiar Examples
3. Application to a Discussion of Cauchy’s Problem
II. OTHER APPLICATIONS OF THE PRINCIPLE OF DESCENT
1. Descent from m Even to m Odd
2. Properties of the Coefficients in the Elementary Solution
3. Treatment of Non-Analytic Equations
INDEX
