Quantitative unique continuation for parabolic equations with Neumann boundary conditions

2022/02/21 by Yueliang Duan, Lijuan Wang, Duan, Yueliang +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.2202.10200

openalex publication_date 2022/02/21 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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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