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

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Abstract

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.

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Acknowledgements

The authors would like to express their sincere thanks to Prof. Mingxin Wang and the anonymous reviewers for their helpful comments and suggestions. The work is partially supported by PRC grant NSFC 11371310, 11401515, the University Science Research Project of Jiangsu Province No. 12KJB110020.

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Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

    Ling Zhou & Zuhan Liu

  2. Dept. of Applied Mathematics, Nanjing Univ. of Finance & Economics, Nanjing, 210023, China

    Shan Zhang

Authors
  1. Ling Zhou
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  2. Shan Zhang
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  3. Zuhan Liu
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Correspondence to Ling Zhou.

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Zhou, L., Zhang, S. & Liu, Z. A Reaction-Diffusion-Advection Equation with a Free Boundary and Sign-Changing Coefficient. Acta Appl Math 143, 189–216 (2016). https://doi.org/10.1007/s10440-015-0035-0

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  • DOI: https://doi.org/10.1007/s10440-015-0035-0

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