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carleman inequality

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Exact null internal controllability for the heat equation on unbounded convex domains ∗
Viorel Barbu
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 1 / January 2014

Published online by Cambridge University Press:

27 January 2014, pp. 222-235

Print publication:

January 2014
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The liner parabolic equation \hbox{$\frac{\pp y}{\pp t}-\frac12\,\D y+F\cdot\na y={\vec{1}}_{\calo_0}u$} $\frac{∂y}{∂t} - \frac{1}{2} Δy + F \cdot \nabla y = 1_{𝒪_{0}} u$ with Neumann boundary condition on a convex open domain 𝒪 ⊂ ℝdwith smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of 𝒪which 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.

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Exact null internal controllability for the heat equation on unbounded convex domains ∗

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Exact null internal controllability for the heat equation on unbounded convex domains∗

Exact null internal controllability for the heat equation on unbounded convex domains ∗