Exact null internal controllability for the heat equation on unbounded convex domains
ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 1, p. 222-235

The linear parabolic equation $\frac{\partial y}{\partial t}-\frac{1}{2}\phantom{\rule{0.166667em}{0ex}}\Delta y+F·\nabla y={\mathbb{1}}_{{𝒪}_{0}}u$ with Neumann boundary condition on a convex open domain $𝒪\subset {ℝ}^{d}$ with smooth boundary is exactly null controllable on each finite interval if ${𝒪}_{0}$ is an open subset of $𝒪$ which contains a suitable neighbourhood of the recession cone of $\overline{𝒪}$. Here, $F:{ℝ}^{d}\to {ℝ}^{d}$ is a bounded, ${C}^{1}$-continuous function, and $F=\nabla g$ where $g$ is convex and coercive.

DOI : https://doi.org/10.1051/cocv/2013062
Classification:  93B07,  35K50,  47D07
@article{COCV_2014__20_1_222_0,
author = {Barbu, Viorel},
title = {Exact null internal controllability for the heat equation on unbounded convex domains},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {20},
number = {1},
year = {2014},
pages = {222-235},
doi = {10.1051/cocv/2013062},
zbl = {1282.93046},
mrnumber = {3182698},
language = {en},
url = {http://www.numdam.org/item/COCV_2014__20_1_222_0}
}

Barbu, Viorel. Exact null internal controllability for the heat equation on unbounded convex domains. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 1, pp. 222-235. doi : 10.1051/cocv/2013062. http://www.numdam.org/item/COCV_2014__20_1_222_0/

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