Observability Inequalities for the Heat Equation with Bounded Potentials on the Whole Space
Observability Inequalities for the Heat Equation with Bounded Potentials on the Whole Space
复制标题
DOI：
10.1137/19m1296847
复制
发表时间：
2019-10
期刊：
影响因子：
--
通讯作者：
Yueliang Duan;Lijuan Wang;Can Zhang
中科院分区：
文献类型：
--
作者：
Yueliang Duan;Lijuan Wang;Can Zhang
本文建立了具有有界势的热方程在全空间上的一个能观性不等式。粗略地说，这种不等式是指解的总能量可以由分布在整个空间的子域内的能量来控制。该不等式的证明主要采用抛物频率函数法，它在证明抛物型方程解的唯一延拓性方面起着重要作用。作为直接应用，我们证明了具有有界势的热方程在整个空间上零能控性是成立的。
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy localized in a subdomain, which is equidistributed over the whole space. The proof of this inequality is mainly adapted from the parabolic frequency function method, which plays an important role in proving the unique continuation property for solutions of parabolic equations. As an immediate application, we show that the null controllability holds for the heat equation with bounded potentials on the whole space.