Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 268, Issue 7, Pages 3880-3902Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2019.10.009
Keywords
Lattice Lotka-Volterra system; Traveling waves; Speed selection
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Funding
- Canada NSERC [RGPIN2016-04509]
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In this paper we study speed selection for traveling wavefronts of the lattice Lotka-Volterra competition model. For the linear speed selection, by constructing new types of upper solutions to the system, we widely extend the results in the literature. We prove that, for the nonlinear speed selection, the wavefront of the first species decays with a faster rate at the far end. This enables us to construct novel lower solutions to establish the existence of pushed wavefronts, a topic that has been understudied. We raise a new conjecture related to the classical Hosono's version of the diffusive system and our numerical simulations help to confirm it, while our rigorous results only provide a partial answer. (C) 2019 Elsevier Inc. All rights reserved.
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