About solvability of initial problem for differential equation with maximum
Journal Title: Дослідження в математиці і механіці - Year 2015, Vol 20, Issue 1
Abstract
Initial value problem for differential equation with maximum is considered. Sufficient conditions of existence and uniqueness solution for this problem are presented.
Authors and Affiliations
A. N. Vityuk, O. D. Kichmarenko, K. Yu. Sapozhnikova
Keywords
Related Articles
- EP ID EP417159
- DOI -
- Views 92
- Downloads 0
Generalization of averaging conditions in the optimal control problem with fast and slow variables
The optimal control problem is described by the system of differential equations with fast and slow variables and by the terminal criterion of quality. There is a generalization of averaging conditions. There is proved t...
Partial averaging of the systems on time scales
The scheme of partial averaging of systems with small parameter on time scales was established. A proximity of solutions of given and partially averaged system of equations was proved under sufficiently general condition...
About one solving method of the contact problem for an elastic semi-infinite layer
It is solved the contact problem on the action of a circular stamp with an extra-central power on the elastic semi-infinite layer. On the lateral and lower side of the layer the conditions of the smooth contact are given...
Approximation of solutions to the optimal control problem for the impulsive system with maximum
This paper presents the averaging method for two problems: impulsive system with maximum and for the optimal control problem of this kind of system. For the first problem the Krylov–Bogolyubov’s theorem is generalized. F...
TWO-SIDED APPROXIMATIONS METHOD AND ROTHE METHOD FOR SOLVING PROBLEMS FOR THE ONE-DIMENSIONAL SEMILINEAR HEAT EQUATION
We consider the first initial-boundary problem for the one-dimensional semilinear heat equation. Based on the modified Rothe method at each time layer the original non-stationary problem is replaced by a nonlinear bounda...