World Academy of Science, Engineering and Technology
Published September 1, 2017 | Version 10008144
Journal article Open

A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society

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This paper is concerned with a system of
Hamilton-Jacobi-Bellman equations coupled with an autonomous
dynamical system. The mathematical system arises in the differential
game formulation of political economy models as an infinite-horizon
continuous-time differential game with discounted instantaneous
payoff rates and continuously and discretely varying state variables.
The existence of a weak solution of the PDE system is proven and
a computational scheme of approximate solution is developed for a
class of such systems. A model of democratization is mathematically
analyzed as an illustration of application.

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