scholarly journals Solutions in the large for multi-dimensional non linear partial differential equations of first order

1965 ◽  
Vol 15 (2) ◽  
pp. 1-35 ◽  
Author(s):  
Avron Douglis
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
Non Linear

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 On the theory of the solution of a system of simultaneous non-linear partial differential equations of the first order

1876 ◽  
Vol 24 (164-170) ◽  
pp. 337-344
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Original Equation ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Linear Partial Differential Equations ◽  
Non Linear

Given an equation of the form z = ϕ ( x 1 , x 2 , . . . x n+r , a 1 , a 2 ,... a r , a + r + 1 ), we obtain by differentiation with respect to each of the n + r variables n + r equations, together with the original equation n + r + 1 equations, from which, eliminating the r + 1 constants, we have a system of n nonlinear partial differential equations. Conversely, given a system of n non-linear partial differential equations with n + r independent variables, if there exists an equation

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