Minimax Theory and its Applications 05 (2020), No. 2, 369--381
Copyright Heldermann Verlag 2020
Hamilton-Jacobi Equations for Neutral-Type Systems: Inequalities for Directional Derivatives of Minimax Solutions
Nikolai Yu. Lukoyanov
Krasovskii Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, Yekaterinburg, Russia
nyul@imm.uran.ru
Anton R. Plaksin
Krasovskii Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, Yekaterinburg, Russia
a.r.plaksin@gmail.com
The paper deals with the Hamilton-Jacobi equation in coinvariant derivatives arising in optimal control problems and differential games for dynamical systems described by differential equations of neutral type. On the basis of a suitable definition of directional derivatives, an infinitesimal criterion of the minimax (generalized) solution of this equation is given.
Keywords: Optimal control, Hamilton-Jacobi equations, neutral-type systems, minimax solutions.
MSC: 49L99, 49J52, 49J21.
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