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It is well known that both the heat equation with Dirichlet or Neumannboundary conditions are null controlable as soon as the control acts in a nontrivial domain (i.e. a set of positive measure, see [10, 11, 12, 1, 6]. In thisarticle, we show that for any couple of initial data (u0, v0) we can achievethe null control for both equations (Dirichlet and Neumann boundary conditionsrespectively) simultaneously with the same control function for both equations.

Simultaneous control for the heat equation with dirichlet and neumann boundary conditions