scholarly journals Linear Partial Differential Equations of First Order as Bi-Dimensional Inverse Moments Problem

2015 ◽  
Vol 06 (06) ◽  
pp. 979-989 ◽  
Author(s):  
Maria Beatriz Pintarelli
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
Moments Problem

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.

III. On the differential equations of dynamics. A sequel to a paper on simultaneous differential equations

1863 ◽  
Vol 12 ◽  
pp. 420-424
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamical Problem ◽  
General Character ◽  
Partial Differential ◽  
Central Function ◽  
First Order ◽  
Linear Partial Differential Equations

Jacobi in a posthumous memoir, which has only this year appeared, has developed two remarkable methods (agreeing in their general character, but differing in details) of solving non-linear partial differential equations of the first order, and has applied them in connexion with that theory of the differential equations of dynamics which was established by Sir W. R. Hamilton in the 'Philosophical Transactions’ for 1834-35. The knowledge, indeed, that the solution of the equation of a dynamical problem is involved in the discovery of a single central function, defined by a single partial differential equation of the first order, does not appear to have been hitherto (perhaps it will never be) very fruitful in practical results.

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