A quantitative strong unique continuation property of a diffusive SIS model

Taige Wang; Dihong Xu

doi:10.3934/dcdss.2022024

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2022, Volume 15, Issue 6: 1599-1614. Doi: 10.3934/dcdss.2022024

This issue Previous Article Local indirect stabilization of same coupled evolution systems through resolvent estimates Next Article

A quantitative strong unique continuation property of a diffusive SIS model

Taige Wang^1, , and
Dihong Xu^2,

1.
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
2.
College of Engineering, Huazhong Agricultural University, Wuhan 430070, China

^* Corresponding author: Taige Wang
^* Corresponding author: Taige Wang

Received: August 1, 2021

Revised: December 1, 2021

Early access: February 18, 2022

Published online: June 1, 2022

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Abstract

This article is concerned with a strong unique continuation property of solutions for a diffusive SIS (Susceptible - Infected - Susceptible, or SI) model, which belongs to a type of observability inequalities in a time interval $ [0, T] $. That is, if one can observe solution on a convex and connected bounded open set $ \omega $ in a bounded domain $ \Omega $ at time $ t = T $, then the norms of solution on $ [0,T) $ on $ \Omega $ are observable. In our discussion, boundary condition is a homogeneous Dirichlet one (hostile boundary condition).

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Mathematics Subject Classification: Primary: 35K61, 93B07.

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