Exact null internal controllability for the heat equation on unbounded convex domains∗. (6th February 2014)

• Record Type: Journal Article
• Authors: Barbu, Viorel
• Is Part Of: ESAIM. Volume 20:Number 1(2014:Jan.)
• Page Start: 222
• Page End: 235
• Publication Date: 2014-02-06
• Subjects: Parabolic equation, -- null controllability, -- convex set, -- Carleman inequality; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013062
• Languages: English
• ISSNs: 1292-8119

Abstract

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.