Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 28, Issue 3, Pages 1051-1067Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2010.28.1051
Keywords
Semilinear equations; asymptotic behavior; ecology; large advection
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Funding
- NSF
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Limiting profiles of solutions to a 2x2 Lotka-Volterra competition-diffusion-advection system, when the strength of the advection tends to infinity, are determined. The two species, competing in a heterogeneous environment, are identical except for their dispersal strategies: One is just random diffusion while the other is smarter - a combination of random diffusion and a directed movement up the environmental gradient. With important progress made, it has been conjectured in [2] and [3] that for large advection the smarter species will concentrate near a selected subset of positive local maximum points of the environment function. In this paper, we establish this conjecture in one space dimension,with the peaks located and the limiting profiles determined, under mild hypotheses on the environment function.
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