@article{e6b4630f0ba94beeaa9110d0f5b51c2d,
title = "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.",
keywords = "Diffusive SIS model, Fisher/KPP equation, Global stability, Initial-boundary value problem",
author = "Fang Wang and Ling Xue and Kun Zhao and Xiaoming Zheng",
note = "Funding Information: The authors would like to thank the anonymous referees for their valuable comments and suggestions which help substantially improve the quality of the paper. F. Wang was partially supported by the National Natural Science Foundation of China (No. 12001064 ), the Natural Science Foundation of Hunan Province (No. 2019JJ50659 ), the Hunan Province Education Department (No. 20B006 ), and the Double First-class International Cooperation Expansion Project (No. 2019IC39 ). L. Xue was partially supported by the Fundamental Research Funds for the Central Universities of China (No. 3072020CFT2402 ). K. Zhao was partially supported by the Simons Foundation Collaboration Grant for Mathematicians (No. 413028 ). Funding Information: The authors would like to thank the anonymous referees for their valuable comments and suggestions which help substantially improve the quality of the paper. F. Wang was partially supported by the National Natural Science Foundation of China (No. 12001064), the Natural Science Foundation of Hunan Province (No. 2019JJ50659), the Hunan Province Education Department (No. 20B006), and the Double First-class International Cooperation Expansion Project (No. 2019IC39). L. Xue was partially supported by the Fundamental Research Funds for the Central Universities of China (No. 3072020CFT2402). K. Zhao was partially supported by the Simons Foundation Collaboration Grant for Mathematicians (No. 413028). Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2021",
month = feb,
day = "25",
doi = "10.1016/j.jde.2020.11.031",
language = "English",
volume = "275",
pages = "391--417",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Journal of Differential Equations",
}