A quantitative strong unique continuation property of a diffusive SIS model

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ [0, T] $\end{document}</tex-math></inline-formula>. That is, if one can observe solution on a convex and connected bounded open set <inline-formula><tex-math id="M2">\begin{document}$ \omega $\end{document}</tex-math></inline-formula> in a bounded domain <inline-formula><tex-math id="M3">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> at time <inline-formula><tex-math id="M4">\begin{document}$ t = T $\end{document}</tex-math></inline-formula>, then the norms of solution on <inline-formula><tex-math id="M5">\begin{document}$ [0,T) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M6">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> are observable. In our discussion, boundary condition is a homogeneous Dirichlet one (hostile boundary condition).</p>