Work

Quantitative unique continuation and observability on an equidistributed set for the diffusion equation in $ \mathbb R^N $

Year: 2025

Type: article

Abstract: In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space $ \mathbb R^N $. This kind of observability indicates that the total energy of solutions can be controlled by the energy localized in a measurable subset, which is equidistributed over the whole space. The proof of our results is based on an interesting reduction method [21,25], as well as the propagation of smallness for the gradient of solutions to elliptic equations [27].

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025164

Authors: Yueliang Duan, Huaiqiang Yu, Can Zhang

Institutions: Shantou University, Tianjin University, Wuhan University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Awards: G4213695501, G7949349594