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JOURNALS // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta // Archive
Izv. IMI UdGU, 2015 Issue 2(46), Pages 149–154 (Mi iimi315)
Singular characteristics of the piecewise-smooth minimax solution of the equation of Hamilton–Jacobi–Bellman

A. S. Rodinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Science, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Institute of Mathematics and Computer Sciences, Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620083, Russia

Abstract: In this paper we study the properties of the minimax piecewise-smooth solution of the Hamilton–Jacobi–Bellman equation. We raise the question of existence of the singular characteristic and properties of the solution related to it.

Keywords: Hamilton–Jacobi–Bellman's equation, minimax solution, singular set, piecewise-smooth solution, tangent space, Rankin–Hugoniot's condition, singular characteristic.

UDC: 517.977

MSC: 49J20, 49L25

Received: 06.10.2015



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