On the Hamilton-Jacobi-Bellman equations in Banach spaces
- Cite this article as:
- Mete Soner, H. J Optim Theory Appl (1988) 57: 429. doi:10.1007/BF02346162
This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.