Abstract
We investigate the null controllability property for the parabolic Grushin equation with an inverse square singular potential. Thanks to a Fourier decomposition for the solution of the equation, we can reduce the problem to the validity of a uniform observability inequality with respect to the Fourier frequency. Such an inequality is obtained by means of a suitable Carleman estimate, with an adapted spatial weight function. We thus show that null controllability holds in large time, as in the case of the Grushin operator without potential.
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