Null controllability for the semilinear heat equation in unbounded domains

• Dias Bezerra de Menezes, Silvano ^[1] ; Cabanillas Lapa, Eugenio ^[2]
  1. [1] Universidad Federal de Pará

     Universidad Federal de Pará

     Brasil

     
  2. [2] Universidad Nacional Mayor de San Marcos

     Universidad Nacional Mayor de San Marcos

     Perú

     
• Localización: Pesquimat, ISSN-e 1609-8439, ISSN 1560-912X, Vol. 4, Nº. 2, 2001
• Idioma: inglés
• DOI: 10.15381/pes.v4i2.9289
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• Resumen

  • In this paper, we consider the null controllability problem for the semilinear heat equation in an unbounded domain Ω of RN with Dirichlet boundary conditions. The control ís assumed to be distributed along a subdomain w such that the uncontrolled regian Ω\w ís bounded. Using Carleman inequalities we first prove the null controllabitity of the linearized equation. Then, by a fixed point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is globally Lipschitz, the system is null controllable.