Insensitizing Controls for the Parabolic Equation with Equivalued Surface Boundary Conditions  

作　　者：Zhong Qi YIN 

机构地区：[1]School of Mathematics,Sichuan University [2]Department of Mathematics,Sichuan Normal University

出　　处：《Acta Mathematica Sinica,English Series》2012年第12期2373-2394,共22页数学学报（英文版）

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

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.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.

关 键 词：Insensitizing controls parabolic equation equivalued boundary conditions 

分 类 号：O175.26[理学—数学]