scholarly journals Estimates of solutions of hyperbolic systems of differential equations in two independent variables

1962 ◽  
Vol 12 (2) ◽  
pp. 191-197 ◽  
Author(s):  
W. Mlak
Keyword(s):  
Differential Equations ◽  
Hyperbolic Systems ◽  
Independent Variables ◽  
Estimates Of Solutions ◽  
Systems Of Differential Equations ◽  
Two Independent Variables

scholarly journals On the differential equations of H. Lewy

1961 ◽  
Vol 2 (1) ◽  
pp. 11-16
Author(s):  
W. B. Smith-White
Keyword(s):  
Differential Equations ◽  
Special Form ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Independent Variables ◽  
Image Position ◽  
Two Independent Variables

It is known that the theory of Cauchy's problem for differential equations with two independent variables is réducible to the corresponding problem for systems of quasi-linear equations. The reduction is carried further, by means of the theory of characteristics, to the case of systems of equations of the special form first considered by H. Lewy [1]. The simplest case is that of the pair of equationswhere the aii depend on z1 and z2. The problem to be considered is that of finding functions z1(x, y), z2(x, y) which satisfy (1) and which take prescribed values on x + y = 0.

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