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1 results

  • Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains

  • L. de Teresa
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 2 / 1997
    Published online by Cambridge University Press:
    15 August 2002, pp. 125-149
    Print publication:
    1997

  • We consider a semilinear heat equation in an unboundeddomain Ω with partially known initial data. The insensitizing problemconsists in finding a control function such that some functional of thestate is locally insensitive to the perturbations of these initial data. Forbounded domains Bodart and Fabre proved the existence of insensitizing controls of the norm of the observation of the solution in an opensubset of the domain. In this paper we prove similar results when Ω isunbounded. We consider the problem in bounded domains of the formΩr = Ω ∩ Br where Br denotes the ball centered in zero of radius r Weshow that for r large enough the control proposed by Bodart and Fabrefor the problem in Ωr , provides an insensitizing control for our problemin Ω.