Local Cauchy problem for linear partial differential equations with analytic coefficients

1969 ◽  
pp. 72-100
Author(s):  
F. Treves
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Linear Partial Differential Equations

scholarly journals The Cauchy Problem For Linear Partial Differential Equations With Restricted Boundary Conditions

1956 ◽  
Vol 8 ◽  
pp. 426-431 ◽  
Author(s):  
E. P. Miles ◽  
Ernest Williams
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Cauchy Data ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
The Cauchy Problem ◽  
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We shall discuss solutions of linear partial differential equations of the form1where Ψ is an ordinary differential operator of order s with respect to t. Our first theorem gives a solution of (1) for the Cauchy data;2j = 1,2, ߪ,s − 1,whenever the function P is annihilated by a finite iteration of the operator Φ.

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