Null controllability of a parabolic equation involving the Grushin operator in some multi-dimensional domains. (English) Zbl 1282.35201
Summary: We study the null controllability of the linear parabolic equation involving the Grushin operator \(G_s=\varDelta_x+| x|^{2s}\varDelta_y(s>0)\), in the domain \(\varOmega =(-1,1)^{N_1}\times (0,1)^{N_2}\subset \mathbb R^{N_1}\times\mathbb R^{N_2}\), \(N_1\), \(N_2\geq 1\), under an additive control supported in an open subset \({\omega}\) of \(\varOmega\). We prove that the equation is null controllable in any positive time for \(s<1\) and not null controllable for \(s>1\). When \(s=1\), a positive minimal time is required for null controllability.
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