A Viscosity Solution Approach to the Infinite-Dimensional HJB Equation Related to a Boundary Control Problem in a Transport Equation
Résumé
The paper concerns the infinite-dimensional Hamilton–Jacobi–Bellman equation related to an optimal control problem regulated by a linear transport equation with boundary control. A suitable viscosity solution approach is needed in view of the presence of the unbounded control-related term in the state equation in the Hilbert setting. An existence-and-uniqueness result is obtained.