Approximate models for nonlinear control and Hamilton-Jacobi-Bellman equations in non-reflexive banach spaces

In many applications of control and games theory we often encounter evolutionary partial differential equations, solutions of which are not smooth enough to satisfy these equations in the classical sense. A classical example is provided by Hamilton-Jacobi-Bellman equations that describe dynamics of value/cost functions which may not be differentiable everywhere. This paper is devoted to the analysis of such situations in both deterministic and stochastic cases.