线性偏微分方程中的柯西问题讲义（英文版） [Lectures on Cauchy's Problem in Linear Partial Differential Equations]

定　　价：98 元

丛书名：世界学术经典丛书

• 作者：（法）阿达马著
• 出版时间：2016/2/1
• ISBN：9787040448047
• 出 版 社：高等教育出版社

• 中图法分类：O175 
• 页码：283
• 纸张：胶版纸
• 版次：1
• 开本：16K

内容简介

　　《线性偏微分方程中的柯西问题讲义（英文版）》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。

目 录

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 CONOID．

THE 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 2ml VARIABLES

1． GENERAL FORMULAE

2． FAMILIAR EXAMPLES

3． APPLICATION TO A DISCUSSION OF CAUCHY'S PROBLEM

II． OTHER APPLICATIONS OF THE PRINCIPLE OF DESCENT

1． DESCENT FROM zn EVEN TO m ODD

2． PROPERTIES OF THE COEFFICIENTS IN THE ELEMENTARY SOLUTION

3． TREATMENT OF NON-ANALYTIC EQUATIONS

INDEX