Viability kernels and capture basins of sets under differential inclusions (Q2753232)

This paper investigates a characterization of viability kernels and capture basins of a target as the unique closed set satisfying geometrical conditions of tangential form (or equivalently of normal form). This is an abstract result generalizing already the obtained method (by Frankowska) for semicontinuous solutions of Hamilton-Jacobi equations.NEWLINENEWLINENEWLINEThe present paper gives a new abstract framework which is very useful for studying not only value functions of Mayer's problem (of Frankowska's works) but also barrier properties, optimal evolutionary controls, episolutions to Hamilton-Jacobi-Bellman inequalities, bilateral viscosity solutions.