Exact null internal controllability for the heat equation on unbounded convex domains∗. (6th February 2014) - Barbu, Viorel
Abstract : The liner parabolic equation\hbox{$\frac{\pp y}{\pp t}-\frac12\, \D y+F\cdot\na y={\vec{1}}_{\calo_0}u$} ∂y ∂t − 1 2   Δy + F · ∇ y = 1 𝒪 0 u with Neumann boundary condition on a convex open domain 𝒪 ⊂ ℝ d with smooth boundary is exactly null controllable on each finite interval if 𝒪0 is an open subset of 𝒪 which contains a suitable neighbourhood of the recession cone of\hbox{$\ov\calo$} 𝒪 . Here, F : ℝ d  → ℝ d is a bounded, C 1 -continuous function, and F  = ∇ g, where g is convex and coercive.