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–Robbiano iteration, based on a new estimate for partial sum of the eigenfunctions of the elliptic operator with equivalued surface boundary conditions.