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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Controlabilidade Finito-Aproximada e Nula para a Equação do Calor Semilinear / Controlabilidade Finito-Aproximada e Nula para a Equação do Calor Semilinear

Pires, Elielson Mendes 02 July 2011 (has links)
Made available in DSpace on 2015-05-15T11:46:02Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 425597 bytes, checksum: 2cb5c42e376ba77764139fbc3fcdaf15 (MD5) Previous issue date: 2011-07-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / We consider the semilinear heat equation involving gradient terms in a bounded domain of Rn. It is assumed the non-linearity is globally Lipschitz. We prove that the system is approximately controllable when the control acts on a bounded subset of the domain. The proof uses a variant of a classical fixed point method and is a simpler alternative to the earlier proof existing in the literature by means of the penalization of an optimal control problem. We also prove that the control may be built so that, in addition to the approximate controllability requirement, it ensures that the state reaches exactly a finite number of constraints. / Consideremos a equação do calor semilinear envolvendo termos do gradiente em um domínio limitado do Rn. Assumimos que a não-linearidade é globalmente Lipschtz. Usando o método do ponto fixo, provamos que o sistema é finito-aproximadamente controlável e nulamente controlável, quando o controle age em um subconjunto não vazio do domínio.

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