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

2020/01/07 by Guojie Zheng, Zheng, Guojie, Dihong Xu +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2001.01882

openalex publication_date 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 L²(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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