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

Published online by Cambridge University Press:  27 January 2014

Viorel Barbu
Viorel Barbu*
Affiliation:
Al.I. Cuza University and Octav Mayer Institute of Mathematics (Romanian Academy), Iaşi, Romania. vbarbu41@gmail.com
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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 ⊂ 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.

Keywords

Parabolic equationnull controllabilityconvex setCarleman inequality

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 1 , January 2014 , pp. 222 - 235
Copyright
© EDP Sciences, SMAI, 2014

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