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

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.