Stabilization to a positive equilibrium for some reaction–diffusion systems |
| |
Institution: | 1. Department of Mathematics, Tamkang University, Tamsui, New Taipei City 251301, Taiwan;2. Department of Mathematics, National Chung Cheng University, Min-Hsiung, Chia-Yi 62102, Taiwan;3. Department of Basic Sciences, Kyushu Institute of Technology, Kitakyushu, Fukuoka 804-8550, Japan |
| |
Abstract: | The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory. |
| |
Keywords: | Stabilization Equilibrium Reaction–diffusion system Entire solution Lyapunov functional |
本文献已被 ScienceDirect 等数据库收录! |
|