Optimal Control And Controllability Of A Phase Field System With One Control Force

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We investigate the relation between optimal control and controllability for a phase field system modeling the solidification process of pure materials in the case that only one control force is used. Such system is constituted of one energy balance equation, with a localized control associated to the density of heat sources and sinks to be determined, coupled with a phase field equation with the classical nonlinearity derived from the two-well potential. 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