The \(L^\infty\)-null controllability of parabolic equation with equivalued surface boundary conditions (Q2852342)

The \(L^\infty\)-null controllability of the parabolic equation with equivalued surface boundary conditions in \(\Omega\times[0,T]\) is obtained. The control is supported in the product of an open subset of \(\Omega\) and a subset of \([0,T]\) with positive measure. First, the authors give some preliminaries and prove the observability estimate on the partial sums of eigenfunctions of the elliptic operator with equivalued surface boundary condition. Then, the authors give the proofs of the two lemmas based on which the estimate for the eigenfunctions of the elliptic operator with equivalued boundary surface boundary conditions is established. In the final part of the paper, the main result is obtained by the method of Lebeau-Robbiano iteration with the use of the lemmas.