Differential Games in a Banach Space on a Fixed Chain

2021 ◽  
Vol 82 (11) ◽  
pp. 2006-2023
Author(s):  
A. V. Chernov
Keyword(s):  
Banach Space ◽  
Differential Games

Linear differential games in a banach space

1997 ◽  
Vol 33 (5) ◽  
pp. 694-699
Author(s):  
V. V. Ostapenko ◽  
I. P. Grabovoi
Keyword(s):  
Banach Space ◽  
Differential Games ◽  
Linear Differential Games ◽  
Linear Differential

scholarly journals Differential games in a Banach space on a fixed chain

2020 ◽  
Vol 12 (3) ◽  
pp. 89-118
Author(s):  
Андрей Владимирович Чернов ◽  
Andrey Chernov
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Electric Field ◽  
Differential Games ◽  
Sufficient Conditions ◽  
Partial Differential ◽  
Time Segment ◽  
Cost Functional

The paper is devoted to obtaining the sufficient conditions for existence of epsilon-equilibrium in the sense of piecewise program strategies in antagonistic games associated with nonlinear non-autonomous controlled differential equation in a Banach space and cost functional of a general enough form. The concept of piecewise program strategies in such a game is defined on the base of a concept of Volterra set chain for a right-hand operator of the corresponding integral equation controlled by the opponent players and according to a given partition of the time segment. As example we consider the game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of electric field in a semiconductor.

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