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

Viorel Barbu

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 1, page 222-235
  • ISSN: 1292-8119

Abstract

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The liner parabolic equation y t - 1 2 𝔻 y + F · y = 1 → 0 u ∂y ∂t − 1 2   Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.

How to cite

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Barbu, Viorel. "Exact null internal controllability for the heat equation on unbounded convex domains." ESAIM: Control, Optimisation and Calculus of Variations 20.1 (2014): 222-235. <http://eudml.org/doc/272944>.

@article{Barbu2014,
abstract = {The liner parabolic equation $\frac\{y\}\{t\}-\frac\{1\}\{2\}\,\mathbb \{D\}y+F\cdot y=\{\vec\{1\}\}_\{_0\}u$ ∂y ∂t − 1 2   Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if &#x1d4aa;0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of $$ x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.},
author = {Barbu, Viorel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {parabolic equation; null controllability; convex set; Carleman inequality},
language = {eng},
number = {1},
pages = {222-235},
publisher = {EDP-Sciences},
title = {Exact null internal controllability for the heat equation on unbounded convex domains},
url = {http://eudml.org/doc/272944},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Barbu, Viorel
TI - Exact null internal controllability for the heat equation on unbounded convex domains
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 1
SP - 222
EP - 235
AB - The liner parabolic equation $\frac{y}{t}-\frac{1}{2}\,\mathbb {D}y+F\cdot y={\vec{1}}_{_0}u$ ∂y ∂t − 1 2   Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if &#x1d4aa;0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of $$ x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.
LA - eng
KW - parabolic equation; null controllability; convex set; Carleman inequality
UR - http://eudml.org/doc/272944
ER -

References

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