The constructive solution of the cauchy problem for linear systems of partial difference or differential equations with constant coefficients

2001 ◽  
Author(s):  
Ulrich Oberst ◽  
Franz Pauer
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Systems ◽  
Partial Difference ◽  
Constructive Solution ◽  
The Cauchy Problem ◽  
Constant Coefficients

scholarly journals On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Malkhaz Ashordia ◽  
Inga Gabisonia ◽  
Mzia Talakhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Unique Solvability ◽  
Sufficient Conditions ◽  
The Cauchy Problem ◽  
Generalized Ordinary Differential Equations

AbstractEffective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

On the solution of Kac-type partial differential equations

1994 ◽  
Vol 31 (A) ◽  
pp. 311-324
Author(s):  
Mátyás Arató
Keyword(s):  
Stochastic Process ◽  
Cauchy Problem ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Explicit Form ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
The Cauchy Problem ◽  
Constant Coefficients

The Cauchy problem in the form of (1.11) with linear and constant coefficients is discussed. The solution (1.10) can be given in explicit form when the stochastic process is a multidimensional autoregression (AR) type, or Ornstein–Uhlenbeck process. Functionals of (1.10) form were studied by Kac in the Brownian motion case. The solutions are obtained with the help of the Radon–Nikodym transformation, proposed by Novikov [12].

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