This article is cited in 5 papers

On the continuous extension of a generalized solution of the Hamilton-Jacobi equation by characteristics that form a central field of extremals

N. N. Subbotina^ab, L. G. Shagalova<sup>a

a</sup> Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg

Abstract: The Cauchy problem for the Hamilton-Jacobi equation with state constraints is considered. A justification for a construction of a generalized solution with given structure is provided. The construction is based on the method of characteristics and on solutions of problems related to calculus of variations.

Keywords: Hamilton-Jacobi equations, method of characteristics, viscosity solutions, minimax solutions, calculus of variations, extremals.

UDC: 517.952+517.97

Received: 12.03.2015

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2016, 293, suppl. 1, S183–S198

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