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.
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