Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 11, Issue 4, Pages 2302-2313Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2009.07.005
Keywords
Entire solution; Traveling wave solutions; KPP equation; Nonlocal dispersal
Categories
Funding
- NSFC [10871085]
- NSF of Gansu Province of China [0710RJZA020]
- Lanzhou University [LZULL200807]
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This paper is concerned with entire solutions of the Fisher-KPP equation with nonlocal dispersal, i.e., u(t) =J * u - u + f(u), which is a one-dimensional nonlocal version of the Fisher-KPP equation describing the spatial spread of a mutant in a given population and the dispersion of the genetic characters is assumed to follow a nonlocal diffusion law modeled by a convolution operator. Here the entire solutions are defined in the whole space and for all time t is an element of R. A comparison principle is employed to establish the existence of entire solutions by combining two traveling wave solutions with different speeds and coming from both ends of the real axis and some spatially independent solutions. The main difficulty is that a lack of regularizing effect occurs. This is probably the first time the existence of entire solutions of reaction equations with nonlocal dispersal has been studied. (C) 2009 Elsevier Ltd. All rights reserved.
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