%0 Journal Article %T Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations %+ Institut de Mathématiques de Toulouse UMR5219 (IMT) %A Raymond, Jean-Pierre %A Zidani, H. %< avec comité de lecture %@ 0095-4616 %J Applied Mathematics and Optimization %I Springer Verlag (Germany) %V 39 %N 2 %P 143-177 %8 1999 %D 1999 %R 10.1007/s002459900102 %K Optimal control %K Nonlinear boundary controls %K Semilinear parabolic equations %K Pontryagin's minimum principle %K Unbounded controls %Z Mathematics [math]/Optimization and Control [math.OC]Journal articles %X 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. %G English %L hal-01254052 %U https://ensta-paris.hal.science/hal-01254052 %~ ENSTA %~ UNIV-TLSE2 %~ UNIV-TLSE3 %~ CNRS %~ INSA-TOULOUSE %~ INSMI %~ IMT %~ UT1-CAPITOLE %~ TDS-MACS %~ INSA-GROUPE %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP