Infinite Horizon Optimal Control for a General Class of Semilinear Parabolic Equations

Source abstract

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 $$L^2$$ L 2 in space. These results rely on a new $$L^\infty$$ L ∞ estimate for nonlinear parabolic equations in an essential manner.