| Abstract: |
| Classical theory predicts that for two competing populations subject to a constant downstream drift, the faster disperser will competitively exclude the slower disperser. In the current work, we consider a novel model of a much faster dispersing species, modeled via a $p$-Laplacian operator, competing with a slower disperser. We prove global existence of weak solutions to this model for any positive initial condition, in certain parametric regime. Counterintuitively, we show that while the faster disperser always wins - the much faster disperser could actually lose, for certain initial data. Our results have implications for biodiversity, refuge design, and improved biological control, driven by habitat fragmentation and climate change |
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