论文标题
在一个有限域中的一类抛物线差异不平等的独特延续属性
A unique continuation property for a class of parabolic differential inequalities in a bounded domain
论文作者
论文摘要
本文关注的是，从凸域$ω$提出的抛物线方程中抽象出的前向差异不平等的唯一延续性属性，并有一些规律性和增长条件。我们的结果表明，在任何给定的正时间$ t $的情况下，可以通过在任意开放子集$ω$上在$ω$的任意开放子集$ω$上唯一确定解决方案的值。我们还得出了这种唯一延续的定量性质，即，$ω$的初始数据的$ l^2（ω）$规范的估计值，该数据由在终端时刻$ t = t $的有限开放子集$ω$上的解决方案中进行了多数。
This article is concerned with the unique continuation property of a forward differential inequality abstracted from parabolic equations proposed on a convex domain $Ω$ prescribed with some regularity and growth conditions. Our result shows that the value of the solutions can be determined uniquely by its value on an arbitrary open subset $ω$ in $Ω$ at any given positive time $T$. We also derive the quantitative nature of this unique continuation, that is, the estimate of a $L^2(Ω)$ norm of the initial data on $Ω$, which is majorized by that of solution on the bounded open subset $ω$ at terminal moment $t = T$.
