Unique solvability of the Cauchy problem for certain quasilinear pseudoparabolic equations

1996 ◽  
Vol 60 (3) ◽  
pp. 264-268 ◽  
Author(s):  
A. L. Gladkov
Keyword(s):  
Cauchy Problem ◽  
Unique Solvability ◽  
The Cauchy Problem ◽  
Pseudoparabolic Equations

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.

scholarly journals Asymptotic Solutions of Scalar Integro-Differential Equations with Partial Derivatives and with Fast Oscillating Coefficients

2020 ◽  
Vol 13 (2) ◽  
pp. 287-302
Author(s):  
Burkhan Kalimbetov ◽  
Akisher Temirbekov ◽  
Abdimuhan Tolep
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Unique Solvability ◽  
Regularization Method ◽  
Singularly Perturbed ◽  
Integral Term ◽  
Integro Differential Equation ◽  
The Cauchy Problem ◽  
Oscillating Coefficients

In the paper, ideas of the Lomov regularization method are generalized to the Cauchy problem for a singularly perturbed partial integro-differential equation in the case when the integral term contains a rapidly varying kernel. Regularization of the problem is carried out, the normal and unique solvability of general iterative problems is proved.

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