On viscosity solution of Hamilton-Jacobi-Belman equations

Soumia Saidi; Mustapha Fateh Yarou

doi:10.26637/MJM0701/0009

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

Mathematics Subject Classification:

Mathematics

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Soumia Saidi LMPA Laboratory, Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel-18000, Algeria.
Mustapha Fateh Yarou LMPA Laboratory, Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel-18000, Algeria. https://orcid.org/0000-0003-4083-1813

Pages: 42-49
Date Published: 01-01-2019
Vol. 7 No. 01 (2019): Malaya Journal of Matematik (MJM)

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