| Abstract: |
| Propagation in heterogeneous and shifting environments is a central problem in ecology and reaction-diffusion theory. Motivated by classical conjectures of Shigesada-Kawasaki and recent works on shifting habitats, we study invasion phenomena in competition systems and their reduction to scalar KPP-type models.
We develop a Hamilton-Jacobi framework based on viscosity solutions to characterize spreading speeds and front dynamics. In particular, we derive a variational formula for the propagation speed and identify regimes where invasion exhibits nonlocal pulling, whereby the spreading speed is determined by distant favorable regions rather than local conditions near the invasion front.
We further extend this framework to non-monotone environments, where the limiting problem may have non-unique solutions. This issue is resolved by introducing appropriate junction conditions and flux-limited solutions in the sense of Imbert-Monneau.
This project is a joint work with Gregoire Nadin, Chang-Hong Wu and Xiao Yu. |
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