Unique solvability of the Cauchy problem for the equations of discrete chiral fields with values in Riemannian manifolds

1985 ◽  
Vol 30 (4) ◽  
pp. 2353-2368 ◽  
Author(s):  
V. I. Shubov
Keyword(s):  
Cauchy Problem ◽  
Unique Solvability ◽  
Riemannian Manifolds ◽  
The Cauchy Problem

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 Statistics of Gaussian packets on metric and decorated graphs

2014 ◽  
Vol 372 (2007) ◽  
pp. 20130145 ◽  
Author(s):  
V. L. Chernyshev ◽  
A. I. Shafarevich
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Solution ◽  
Riemannian Manifolds ◽  
Initial Function ◽  
Time Dependent ◽  
Semiclassical Asymptotics ◽  
Subexponential Growth ◽  
Codimension One ◽  
The Cauchy Problem ◽  
Opposite Situation

We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth.

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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