HJB equations in infinite dimension with locally Lipschitz Hamiltonian and unbounded terminal condition

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.