Multi-type Entire Solutions in a Nonlocal Dispersal Epidemic Model

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• 作者：Li Zhang ; Wan-Tong Li ; Shi-Liang Wu
• 关键词：Entire solutions ; Nonlocal dispersal ; Epidemic model ; Traveling wave solutions ; Asymptotic behavior ; 35K57 ; 37C65 ; 92D30
• 刊名：Journal of Dynamics and Differential Equations
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：28
• 期：1
• 页码：189-224
• 全文大小：747 KB
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• 作者单位：Li Zhang (1)
  Wan-Tong Li (1)
  Shi-Liang Wu (2)
  
  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China
  2. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Ordinary Differential Equations
  Partial Differential Equations
  Applications of Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9222

文摘

This paper deals with entire solutions of a nonlocal dispersal epidemic model. Unlike local (random) dispersal problems, a nonlocal dispersal operator is not compact and the solutions of nonlocal dispersal system studied here lack regularity in suitable spaces, which affects the uniform convergence of the solution sequences and the technique details in constructing the entire solutions. In the monostable case, some new types of entire solutions are constructed by combining leftward and rightward traveling fronts with different speeds and a spatially independent solution. In the bistable case, the existence of many different entire solutions with merging fronts are proved by constructing different sub- and super-solutions. Various qualitative features of the entire solutions are also investigated. A key idea is to characterize the asymptotic behaviors of the traveling wave solutions at infinite in terms of appropriate sub- and super-solutions. Finally, we also obtain the smoothness of the entire solutions in space, i.e., the solutions established in our paper are global Lipschitz continuous in space. Keywords Entire solutions Nonlocal dispersal Epidemic model Traveling wave solutions Asymptotic behavior