UNIQUE CONTINUATION PROPERTY FOR A CLASS OF PARABOLIC DIFFERENTIAL INEQUALITIES IN A BOUNDED DOMAIN

被引：0

作者：

Zheng, Guojie ^{[1
]}

Xu, Dihong ^{[2
]}

Wang, Taige ^{[3
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] Huazhong Agr Univ, Coll Engn, Wuhan 430070, Peoples R China

[3] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 02期

关键词：

Unique continuation; frequency function; differential inequality; THEOREM;

D O I：

10.3934/cpaa.2020280

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with a strong unique continuation property of a forward differential inequality abstracted from parabolic equations proposed on a convex domain Omega prescribed with some regularity and growth conditions. Our results show that the value of the solutions can be determined uniquely by its value on an arbitrary open subset omega in Omega at any given positive time T. We also derive the quantitative nature of this unique continuation, that is, the estimate of a L-2 (Omega) norm of the initial data, which is majorized by that of solution on the bounded open subset w at terminal moment t = T.

引用

页码：547 / 558

页数：12

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