论文标题
一类超强退化抛物线运营商和应用的卡尔曼不平等
Carleman inequality for a class of super strong degenerate parabolic operators and applications
论文作者
论文摘要
在本文中，我们为与一类超强退化抛物线线性问题相关的伴随方程式提供了一个新的Carleman估计。我们的方法考虑了对控制域的标准几何施加，在一般情况下无法删除。此外，我们还应用了上述主要不平等，以研究两个非线性抛物线系统的无效可控性。第一个应用程序涉及一些半线性方程获得的全局无效可控性结果，依赖于固定点参数。在第二个方面，通过使用逆函数定理，还可以实现针对具有非局部项的某些方程的局部零可控性。
In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed in the general situations. Additionally, we also apply the aformentioned main inequality in order to investigate the null controllability of two nonlinear parabolic systems. The first application is concerned a global null controllability result obtained for some semilinear equations, relying on a fixed point argument. In the second one, a local null controllability for some equations with nonlocal terms is also achieved, by using an inverse function theorem.
