Null controllability of Grushin-type operators in dimension two
Karine Beauchard
École Polytechnique, Palaiseau, FrancePiermarco Cannarsa
Università di Roma, ItalyRoberto Guglielmi
Università di Roma 'Tor Vergata', Italy
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Abstract
We study the null controllability of the parabolic equation associated with the Grushin-type operator in the rectangle , under an additive control supported in an open subset of . We prove that the equation is null controllable in any positive time for and that there is no time for which it is null controllable for . In the transition regime and when is a strip , a positive minimal time is required for null controllability. Our approach is based on the fact that, thanks to the particular geometric configuration of , null controllability is closely linked to the one-dimensional observability of the Fourier components of the solution of the adjoint system, uniformly with respect to the Fourier frequency.
Cite this article
Karine Beauchard, Piermarco Cannarsa, Roberto Guglielmi, Null controllability of Grushin-type operators in dimension two. J. Eur. Math. Soc. 16 (2014), no. 1, pp. 67–101
DOI 10.4171/JEMS/428