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

Article type: Research Article

Authors: Lü, Qi | Yin, Zhongqi^;

Affiliations: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China and Basque Center for Applied Mathematics, Mazarredo 14, 48009 Bilbao, Basque Country, Spain. E-mail: [email protected] | Department of Mathematics, Sichuan Normal University, Chengdu 610068, China. E-mail: [email protected]

Note: [] Corresponding author. E-mail: [email protected]

Abstract: 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.

Keywords: L^∞-null controllability, parabolic equation, equivalued surface boundary condition, Lebeau–Robbiano iteration

DOI: 10.3233/ASY-131167

Journal: Asymptotic Analysis, vol. 83, no. 4, pp. 355-378, 2013