Insensitizing Controls for the Parabolic Equation with Equivalued Surface Boundary Conditions

作     者：Zhong Qi YIN 

作者机构：School of MathematicsSichuan University Department of MathematicsSichuan Normal University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第12期

页      面：2373-2394页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10831007 and 60974035) 

主　　题：Insensitizing controls parabolic equation equivalued boundary conditions 

摘      要：This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions~ in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions.