Existence and stability of bistable wavefronts in a nonlocal delayed reaction–diffusion epidemic system
Existence and stability of bistable wavefronts in a nonlocal delayed reaction–diffusion epidemic system
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DOI：
10.1017/s0956792520000078
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发表时间：
2020-03
影响因子：
1.9
通讯作者：
Kun Li;Xiong Li
中科院分区：
文献类型：
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作者：
Kun Li;Xiong Li
本文考虑一类具有非局部时滞的反应扩散传染病系统的单调行波解。利用抽象的存在性结果得到了单调行波解的存在性。通过将非局部时滞系统转化为非时滞系统，并选取适当的小正常数定义一对新的上下解，利用压缩技巧证明了单调行波的渐近稳定性（直至平移）.利用上下解方法和指数渐近稳定性，证明了单调行波解的唯一性和李雅普诺夫稳定性。
In this paper, we consider the monotone travelling wave solutions of a reaction–diffusion epidemic system with nonlocal delays. We obtain the existence of monotone travelling wave solutions by applying abstract existence results. By transforming the nonlocal delayed system to a non-delayed system and choosing suitable small positive constants to define a pair of new upper and lower solutions, we use the contraction technique to prove the asymptotic stability (up to translation) of monotone travelling waves. Furthermore, the uniqueness and Lyapunov stability of monotone travelling wave solutions will be established with the help of the upper and lower solution method and the exponential asymptotic stability.