On viscosity solution of Hamilton-Jacobi-Belman equations

Soumia Saidi1 and Mustapha Fateh Yarou1 *

doi:10.26637/MJM0701/0009

On viscosity solution of Hamilton-Jacobi-Belman equations

Authors :

Soumia Saidi¹ and Mustapha Fateh Yarou^{1 *}

Author Address :

¹LMPA Laboratory, Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel-18000, Algeria.

*Corresponding author.

Abstract :

The paper deals with an optimal control problem governed by a state equation which involves evolution inclusions. These inclusions are formulated through time-dependent maximal monotone operators and the control variable runs in a suitable class of Young measures. We show, in the finite dimensional setting, that the value function of the problem is a viscosity solution of the Hamilton-Jacobi-Bellman problem.

Keywords :

Maximal monotone operator, evolution inclusion, Young measure, control, value function, viscosity solution.

DOI :

10.26637/MJM0701/0009

Article Info :

Received : July 11, 2018; Accepted : December 12, 2018.