论文标题
第四阶半线性抛物线方程的不敏感控制
Insensitizing controls for a fourth order semi-linear parabolic equations
论文作者
论文摘要
本文涉及第四阶半线性抛物线方程的不敏感控制。在这里，初始数据是部分未知的，我们想找到控件，以使特定功能对初始数据的小扰动不敏感。通常，这种问题可以作为非线性级联系统的无效可控性问题。首先，我们将通过全球Carleman估计和双重参数证明线性问题的无效可控性结果。然后，根据Leray-Schauder的固定点定理，我们在半线性情况下得出了级联系统的无效可控性。
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.
