A Reaction-Diffusion-Advection Equation with a Free Boundary and Sign-Changing Coefficient

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• 作者：Ling Zhou ; Shan Zhang ; Zuhan Liu
• 关键词：A free boundary problem ; Spreading ; vanishing dichotomy ; Advection ; Spreading speed ; 35K51 ; 35R35 ; 92B05 ; 35B40
• 刊名：Acta Applicandae Mathematicae
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：143
• 期：1
• 页码：189-216
• 全文大小：1,314 KB
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• 作者单位：Ling Zhou (1)
  Shan Zhang (2)
  Zuhan Liu (1)
  
  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China
  2. Dept. of Applied Mathematics, Nanjing Univ. of Finance & Economics, Nanjing, 210023, China
  
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036
• 卷排序：143

文摘

In this paper we investigate a reaction-diffusion-advection equation with a free boundary and sign-changing coefficient. The main objective is to understand the influence of the advection term on the long time behavior of the solutions. More precisely, we prove a spreading-vanishing dichotomy result, namely the species either successfully spreads to infinity as \(t\rightarrow\infty\) and survives in the new environment, or it fails to establish and dies out in the long run. When spreading occurs, the spreading speed of the expanding front is affected by the advection. In this situation, we obtain best possible upper and lower bounds for the spreading speed of the expanding front. Furthermore, when the environment is asymptotically homogeneous at infinity, these two bounds coincide. Keywords A free boundary problem Spreading-vanishing dichotomy Advection Spreading speed