We study Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space, with Lipschitz coefficients, where the Hamiltonian has superquadratic growth with respect to the derivative of the value function, and the final condition is not bounded. This allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes. The results are applied to a controlled wave equation. © 2014 Elsevier Inc.
Masiero, F., Richou, A. (2014). HJB equations in infinite dimensions with locally Lipschitz Hamiltonian and unbounded terminal condition. JOURNAL OF DIFFERENTIAL EQUATIONS, 257(6), 1989-2034 [10.1016/j.jde.2014.05.026].
HJB equations in infinite dimensions with locally Lipschitz Hamiltonian and unbounded terminal condition
MASIERO, FEDERICA
;
2014
Abstract
We study Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space, with Lipschitz coefficients, where the Hamiltonian has superquadratic growth with respect to the derivative of the value function, and the final condition is not bounded. This allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes. The results are applied to a controlled wave equation. © 2014 Elsevier Inc.
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