Optimal Control and Controllability of a Phase Field System with One Control Force |
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Authors: | F D Araruna J L Boldrini B M R Calsavara |
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Institution: | 1. Departamento de Matemática, Universidade Federal da Paraíba, 58051-900?, Jo?o Pessoa, PB, Brazil 2. Instituto de Matemática, Estatística e Computa??o Científica, Universidade Estadual de Campinas, 13083-970?, Campinas, SP, Brazil 3. Faculdade de Ciências Aplicadas, Universidade Estadual de Campinas, R. Pedro Zaccaria, 1300, CEP 13484-350?, Limeira, SP, Brazil
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Abstract: | 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. We prove that this system has a local controllability property and we establish that a sequence of solutions of certain optimal control problems converges to a solution of such controllability problem. |
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