Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations

Abstract. In this paper we study optimal control problems governed by semilinear parabolic equations. We obtain necessary optimality conditions in the form of an exact Pontryagin's minimum principle for distributed and boundary controls (which can be unbounded) and bounded initial controls. These optimality conditions are obtained thanks to new regularity results for linear and nonlinear parabolic equations.

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