Hamilton-Jacobi-Bellman Equations with Time-Measurable Data and Infinite Horizon
Résumé
In this paper we investigate the existence and uniqueness of weak solutions of the nonautonomous Hamilton-Jacobi-Bellman equation on the domain (0, ∞) × Ω. The Hamiltonian is assumed to be merely measurable in time variable and the open set Ω may be unbounded with nonsmooth boundary. The set Ω is called here a state constraint. When state constraints arise, then classical analysis of Hamilton-Jacobi-Bellman equation lacks appropriate notion of solution because continuous solutions could not exist. In this work we propose a notion of weak solution for which, under a suitable controllability assumption, existence and uniqueness theorems are valid in the class of lower semicontinuous functions vanishing at infinity.
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