scholarly journals Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables

2000 ◽  
Author(s):  
Emil Cornea ◽  
Ralph Howard ◽  
Per-Gunnar Martinsson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Singular Points ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Two Independent Variables

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 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 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

Mixed Problems for Linear Systems of first Order Equations

1958 ◽  
Vol 10 ◽  
pp. 127-160 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Auxiliary Data ◽  
First Order ◽  
Independent Variables ◽  
Mixed Problems ◽  
Linear Partial Differential Equations ◽  
Data Problem ◽  
Hyperbolic Differential Equations

A mixed problem in the theory of partial differential equations is an auxiliary data problem wherein conditions are assigned on two distinct surfaces having an intersection of lower dimension. Such problems have usually been formulated in connection with hyperbolic differential equations, with initial and boundary conditions prescribed. In this paper a study is made of the conditions appropriate to a system of R linear partial differential equations of first order, in R dependent and N independent variables.

scholarly journals An integrable system of partial differential equations on the special linear group

2002 ◽  
Vol 44 (1) ◽  
pp. 83-93
Author(s):  
Peter J. Vassiliou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Group ◽  
Special Linear Group ◽  
Partial Differential ◽  
Special Linear ◽  
First Order ◽  
Independent Variables ◽  
Two Independent Variables

AbstractWe give an intrinsic construction of a coupled nonlinear system consisting of two first-order partial differential equations in two dependent and two independent variables which is determined by a hyperbolic structure on the complex special linear group regarded as a real Lie groupG. Despite the fact that the system is not Darboux semi-integrable at first order, the construction of a family of solutions depending.upon two arbitrary functions, each of one variable, is reduced to a system of ordinary differential equations on the 1-jets. The ordinary differential equations in question are of Lie type and associated withG.

scholarly journals Memoir on the integration of partial differential equations of the second order in three independent variables, when an intermediary integral does not exist in general

1898 ◽  
Vol 62 (379-387) ◽  
pp. 283-285
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
General Feature ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Dependent Variables ◽  
Two Independent Variables

The general feature of most of the methods of integration of any partial differential equation is the construction of an appropriate subsidiary system and the establishment of the proper relations between integrals of this system and the solution of the original equation. Methods, which in this sense may be called complete, are possessed for partial differential equations of the first order in one dependent variable and any number of independent variables; for certain classes of equations of the first order in two independent variables and a number of dependent variables; and for equations of the second (and higher) orders in one dependent and two independent variables.

Sign in / Sign up

Export Citation Format

Share Document