Insensitizing controls for the parabolic equation with equivalued surface boundary conditions
Insensitizing controls for the parabolic equation with equivalued surface boundary conditions
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DOI：
10.1007/s10114-012-1309-3
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发表时间：
2012-11
期刊：
影响因子：
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通讯作者：
Zhongqi Yin
中科院分区：
文献类型：
--
作者：
Zhongqi Yin
本文研究了具有等值面边界条件的抛物型方程的钝感控制的存在性。不敏感问题在于找到一个控制函数，使得方程的某些能量泛函对初始数据的扰动局部不敏感。通常，这个问题可以归结为一个具有等值面边界条件的两个抛物方程的级联系统的部分零能控性问题。与通常边界条件下的问题相比，在本例中，我们需要得到一个新的整体Carleman估计，特别是需要构造一个新的权函数来匹配等值面边界条件。
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.