scholarly journals On the Solution of Non-linear Partial Differential Equations of the Second Order

1891 ◽  
Vol 10 ◽  
pp. 63-70
Author(s):  
John M'Cowan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Independent Variables ◽  
Linear Partial Differential Equations ◽  
General Utility ◽  
Non Linear ◽  
Two Independent Variables

§ 1. It is proposed to discuss in this paper partial differential equations involving two independent variables x and y, and a dependent variable z. The method of reduction which is explained can be applied to certain equations involving more than two independent variables, but such application is subject to too many restrictions to be of much general utility.

scholarly journals On a method for constructing Bergman kernels

1980 ◽  
Vol 29 (4) ◽  
pp. 454-461
Author(s):  
A. Azzam ◽  
E. Kreyszig
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Bergman Kernels ◽  
Order Linear ◽  
Independent Variables ◽  
New Class ◽  
Linear Partial Differential Equations ◽  
Two Independent Variables

AbstractWe establish a method of constructing kernels of Bergman operators for second-order linear partial differential equations in two independent variables, and use the method for obtaining a new class of Bergman kernels, which we call modified class E kernels since they include certain class E kernals. They also include other kernels which are suitable for global representations of solutions (whereas Bergman operators generally yield only local representations).

scholarly journals VII. On the theory of the solution of a system of simultaneous non-linear partial ddifferential equations of the first order

1875 ◽  
Vol 23 (156-163) ◽  
pp. 510-510
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Arbitrary Constant ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
The Given

Given an equation of the form z = ϕ ( x 1 , x 2 , ..... x n+m , a 1 , a 2 ,. . . . a n ), we obtain by differentiation with respect to each of the n + m independent variables x 1 , x 2 , ..... x n+m , and elimination of the n arbitrary constant a 1 , a 2 ,. . . . a n a system of m +1 non-linear partial differential equations of the first order. Of this system the given equation may be said to be "complete primitive.”

scholarly journals IV. On simultaneous partial differential equations

1901 ◽  
Vol 195 (262-273) ◽  
pp. 151-191 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Single Equation ◽  
Second Order ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Two Independent Variables

In this paper, without touching on the question of the existence of integrals of systems of simultaneous partial differential equations, I have given a method by which the problem of finding their complete primitives may he attacked. The cases discussed are two: that of a pair of equations of the first order in two dependent and two independent variables, and that of a single equation of the second order, with one dependent and two independent variables.

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