This article is cited in 1 paper

Method of characteristics for optimal control problems and conservation laws

N. N. Subbotina, E. A. Kolpakova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya str., Yekaterinburg, 620990, Russia

Abstract: In this paper, notions of global generalized solutions of Cauchy problems for the Hamilton–Jacobi–Bellman equation and for a quasilinear equation (a conservation law) are introduced in terms of characteristics of the Hamilton–Jacobi equation. Theorems on the existence and uniqueness of generalized solutions are proved. Representative formulas for generalized solutions are obtained and a relation between generalized solutions of the mentioned problems is justified. These results tie nonlinear scalar optimal control problems and one-dimensional stationary conservation laws.

UDC: 519.857

 English version: Journal of Mathematical Sciences, 2014, 199:5, 588–595

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