The role of the range of dispersal in a nonlocal Fisher-KPP equation: an asymptotic analysis
Keyword(s):
In this paper, we study the asymptotic behavior as [Formula: see text] of solutions [Formula: see text] to the nonlocal stationary Fisher-KPP type equation [Formula: see text] where [Formula: see text] and [Formula: see text]. Under rather mild assumptions and using very little technology, we prove that there exists one and only one positive solution [Formula: see text] and that [Formula: see text] as [Formula: see text] where [Formula: see text]. This generalizes the previously known results and answers an open question raised by Berestycki et al. Our method of proof is also of independent interest as it shows how to reduce this nonlocal problem to a local one. The sharpness of our assumptions is also briefly discussed.
2005 ◽
Vol 37
(04)
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pp. 1075-1093
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2005 ◽
Vol 37
(4)
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pp. 1075-1093
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2010 ◽
Vol 42
(03)
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pp. 834-854
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2013 ◽
Vol 2013
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pp. 1-7
2020 ◽
Vol 5
(1)
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pp. 195-210
Keyword(s):
2017 ◽
Vol 14
(07)
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pp. 1750108
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