Quantitative unique continuation for parabolic equations with Neumann boundary conditions

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2022-02-21 DOI:10.3934/mcrf.2022058

Yueliang Duan, Lijuan Wang, Can Zhang

引用次数: 1

Abstract

In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions of parabolic equations with Neumann boundary conditions in bounded domains. Our proof is mainly based on Carleman commutator estimates and a global frequency function argument, which is motivated from a recent work [5]. As an application, we obtain an observability inequality from measurable sets in time for all solutions of the above equations.

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具有Neumann边界条件的抛物方程的定量唯一延拓

本文建立了有界区域上具有Neumann边界条件的抛物型方程解在一时间点唯一延拓的全局定量估计。我们的证明主要基于Carleman换向子估计和一个全局频率函数参数，该参数来源于最近的一项工作[5]。作为应用，我们得到了上述方程的所有解在时间上的可测集上的一个可观测不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.