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arXiv 2001.018822020-01-07math.OCmath.AP

A unique continuation property for a class of parabolic differential inequalities in a bounded domain

Guojie Zheng, Dihong Xu, Taige Wang

备注：: 14 pages

英文摘要：

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 $t = T$.

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