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Abstract A class of infinite horizon optimal control problems subject to semilinear parabolic equations is investigated. First and second order optimality conditions are obtained, in the presence of constraints on the controls, which can be either pointwise in space-time, or pointwise in time and L² L 2 in space. These results rely on a new L^ L ∞ estimate for nonlinear parabolic equations in an essential manner.
Casas et al. (Fri,) studied this question.