On the Hamilton-Jacobi-Bellman equations in Banach spaces
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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.
Key WordsDistributed control problems viscosity solutions controlled delay equations
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