Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 267, Issue 8, Pages 4890-4921Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2019.05.019
Keywords
Lotka-Volterra type competition; Shifting environment; Nonlocal dispersal; Extinction; Persistence; Spreading speed
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Funding
- NSF of China [11401096]
- Foshan University [CGZ07093]
- NSERC of Canada [RGPIN2016-04665]
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We consider a competitive system with nonlocal dispersals in a 1-dimensional environment that is worsening with a constant speed, reflected by two shifting growth functions. By analyzing the spatial-temporal dynamics of the model system, we are able to identify certain ranges for the worsening speed c, respectively for (i) extinction of both species; (ii) extinction of one species but persistence of the other; (iii) persistence of both species. In the case of persistence of a species, it is achieved through spreading to the direction of favorable environment with certain speed(s), and some estimates of these speeds are also obtained. We also present some numeric simulation results which confirm our theoretical results, and in the mean time, motivate some challenging problems for future work. (C) 2019 Elsevier Inc. All rights reserved.
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