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−12 Δy+F·∇y=1𝒪0u with Neumann boundary condition on a convex open domain 𝒪 ⊂ ℝd 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 : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.