A viscosity solution approach to the infinite dimensional HJB related to   boundary control problem in transport equation
  The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a 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 Hilbertian state equation. An existence-and-uniqueness result is obtained. 
Giorgio Fabbri