一类四阶半线性抛物型方程的钝感控制
Insensitizing controls for a fourth order semi-linear parabolic equations
摘要：
研究了一类四阶半线性抛物型方程的不灵敏控制的存在性。在这里，初始数据是部分未知的，我们希望找到控制，使一个特定的功能是不敏感的初始数据的小扰动。一般来说，这类问题可以转化为非线性级联系统的零能控性问题。我们将首先证明一个线性问题的零可控性结果的整体Carleman估计和对偶参数。然后，利用Leray-Schauder的不动点定理，得到了半线性情形下级联系统的零能控性。
英文摘要：
This paper is concerned with the existence of insensitizing controls for a fourth order semilinear parabolic equation. Here, the initial data is partially unknown, we would like to find controls such that a specific functional is insensitive for small perturbations of the initial data. In general, this kind of problems can be recast as a null controllability problem for a nonlinear cascade system. We will first prove a null controllability result for a linear problem by global Carleman estimates and dual arguments. Then, by virtue of Leray-Schauder's fixed points theorem, we conclude the null controllability for the cascade system in the semi-linear case.
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