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The L∞-null controllability of parabolic equation with equivalued surface boundary conditions

In this paper, we obtain the L∞−null controllability of the parabolic equation with equivalued surface boundary conditions in Ω× [0, T ]. The control is supported in the product of an open subset of Ω and a subset of [0, T ] with positive measure. The main result is obtained by the method of Lebeau-Robianno-type iteration, based on a new estimate for partial sum of the eigenfunctions of the elliptic operator with equivalued surface boundary conditions.