Acta Applicandae Mathematicae

, Volume 159, Issue 1, pp 139–168 | Cite as

Dynamics for a Nonlocal Reaction-Diffusion Population Model with a Free Boundary

  • Yaling Zhao
  • Zuhan Liu
  • Ling ZhouEmail author


In this paper we focus on a nonlocal reaction-diffusion population model. Such a model can be used to describe a single species which is diffusing, aggregating, reproducing and competing for space and resources, with the free boundary representing the expanding front. The main objective is to understand the influence of the nonlocal term in the form of an integral convolution on the dynamics of the species. Precisely, when the species successfully spreads into infinity as \(t\rightarrow \infty \), it is proved that the species stabilizes at a positive equilibrium state under rather mild conditions. Furthermore, we obtain a upper bound for the spreading of the expanding front.


Dynamics A free boundary condition Integral convolution Spreading speed 

Mathematics Subject Classification

35R35 92B05 35B40 



The authors would like to express their sincere thanks to the anonymous reviewers for their helpful comments and suggestions. The work is partially supported by PRC grant NSFC 11771380, 11401515.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mathematical ScienceYangzhou UniversityYangzhouChina

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