On the continuous extension of a generalized solution of the Hamilton–Jacobi equation by characteristics that form a central field of extremals
Nina Nikolaevna Subbotina, Lyubov Gennadievna Shagalova · Proceedings of the Steklov Institute of Mathematics · 2016
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.