Global stabilization and boundary control of generalized Fisher/KPP equation and application to diffusive SIS model

Fang Wang, Ling Xue, Kun Zhao, Xiaoming Zheng

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, the global stabilization of solutions to initial-boundary value problems for the generalized Fisher/KPP equation is studied. It is shown that 1) under the homogeneous Neumann boundary condition, equilibrium states determined by the generalized carrying capacity are globally asymptotically stable; 2) under the Dirichlet-type dynamic boundary condition, the dynamics of solutions is driven/controlled by the boundary data in the large-time limit. As an application, similar results are obtained for the diffusive susceptible-infected-susceptible (SIS) model in mathematical epidemiology.

Original languageEnglish
Pages (from-to)391-417
Number of pages27
JournalJournal of Differential Equations
Volume275
DOIs
StatePublished - Feb 25 2021

Keywords

  • Diffusive SIS model
  • Fisher/KPP equation
  • Global stability
  • Initial-boundary value problem

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