Construction of a generalized solution to an equation that preserves the Bellman type in a given domain of the state space

Abstract

A Cauchy problem is considered for a Hamilton-Jacobi equation that preserves the Bellman type in a spatially bounded strip. Sufficient conditions are obtained under which there exists a continuous generalized (minimax/viscosity) solution to this problem with a given structure in the strip. A construction of this solution is presented. © Pleiades Publishing, Ltd., 2012.