Existence of an extinction wave in the Fisher equation with a shifting habitat
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- by Haijun Hu and Xingfu Zou PDF
- Proc. Amer. Math. Soc. 145 (2017), 4763-4771 Request permission
Abstract:
This paper deals with the existence of traveling wave solutions of the Fisher equation with a shifting habitat representing a transition to a devastating environment. By constructing a pair of appropriate upper/lower solutions and using the method of monotone iteration, we prove that for any given speed of the shifting habitat edge, this reaction-diffusion equation admits a monotone traveling wave solution with the speed agreeing to the habitat shifting speed, which accounts for an extinction wave. This predicts not only how fast but also in what manner a biological species will die out in such a shifting habitat.References
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Additional Information
- Haijun Hu
- Affiliation: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, People’s Republic of China, 410114
- MR Author ID: 875420
- Email: huhaijun2000@163.com
- Xingfu Zou
- Affiliation: Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada, N6A 5B7
- MR Author ID: 618360
- Email: xzou@uwo.ca
- Received by editor(s): October 3, 2016
- Published electronically: July 28, 2017
- Additional Notes: The first author was partially supported by NNSF of China (Nos. 11326116, 11401051) and Hunan Provincial Natural Science Foundation (Nos. 2015JJ3013, 2016JJ1001). The second author was partially supported by NSERC of Canada (No. RGPIN-2016-04665)
- Communicated by: Yingfei Yi
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4763-4771
- MSC (2010): Primary 34C05, 34D20; Secondary 92D40, 92D25
- DOI: https://doi.org/10.1090/proc/13687
- MathSciNet review: 3691993