| Abstract: |
| In this talk, we will discuss the large time behavior of solutions of reaction-diffusion equations and systems with shifting heterogeneities. Such a situation arises in the modeling of population dynamics under an environmental change, due e.g. to global warming. We will be concerned with the extinction or survival of species, and in the latter case in how it spreads ahead of the heterogeneity. While the key issue is whether the species is able to outpace the climate, which may sound relatively straightforward, we will find the picture may quickly become more intricate than expected. In particular, we will see how nonlinear features may strongly impact the outcome due for instance to Allee effects or inter-species competition. In particular, we will see that the size of the initial population may play a crucial part into its survival at large times. |
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