Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 147, Issue 4, Pages 1467-1481Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/14235
Keywords
Nonlocal Fisher-KPP equation; shifting environment; uniqueness of forced waves; global stability
Categories
Funding
- Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)
- Joint Training Ph.D Program of China Scholarship Council [201606180060]
- NSERC of Canada
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This paper deals with the uniqueness and global stability of forced extinction waves for the nonlocal dispersal Fisher-KPP equation in a shifting environment where the favorable habitat is shrinking. Specifically, we first obtain the uniqueness by using the sliding technique and then establish the global exponential stability via the monotone semiflows approach combined with the method of super- and subsolutions. Our developed arguments can also be used to prove the same conclusion for the corresponding random diffusion problem.
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