TY - JOUR
T1 - Global stabilization and boundary control of generalized Fisher/KPP equation and application to diffusive SIS model
AU - Wang, Fang
AU - Zheng, Xiaoming
PY - 2021/2
Y1 - 2021/2
N2 - 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.
AB - 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.
UR - https://doi.org/10.1016/j.jde.2020.11.031
M3 - Article
VL - 275
SP - 391
EP - 417
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
ER -