Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Many physical systems are modeled by monotone PDE, for example, diffusive processes occuring in porous media are often described with this type of equation. We place our attention on optimal control problems whose dynamics are governed by systems of this type which are subject so stochastic forcing. We provide necessary conditions of optimality for such control systems in the case where the nonlinearity is sub/superlinear in terms of co-state variables which satisfy a backward stochastic evolution equation.