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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Cannarsa, P., Guglielmi, R. (2014). Null controllability in large time for the parabolic Grushin operator with singular potential. In: Stefani, G., Boscain, U., Gauthier, JP., Sarychev, A., Sigalotti, M. (eds) Geometric Control Theory and Sub-Riemannian Geometry. Springer INdAM Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-02132-4_6
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DOI: https://doi.org/10.1007/978-3-319-02132-4_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02131-7
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