Limiting profiles of semilinear elliptic equations with large advection in population dynamics
By King-Yeung Lam, Wei-Ming Ni. 2010
60 citations recorded by the source corpus.
Limiting profiles of solutions to a 2$\times$2 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.
Subfields: Mathematical Physics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/b1ede1019388e4ffeb816da0579493dba9c6e3f3
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In Mathematical Physics
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Citations in the corpus
- Dynamics of a reaction-diffusion-advection modelfor two competing species (2012, background): “For more recent progress on (1) and (2) and related models, see [2, 4, 9, 10, 11, 13, 18, 23, 24, 25].”
- Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, background): “For further discussion and detailed derivations of the results described above see [5, 8, 15, 16, 21, 22, 25, 40, 59, 61] and the references therein.”