| Abstract: |
| In 1937, independently, Fisher and KPP (Kolmogorov-Petrovskii-Piskunov) used a simple reaction-diffusion equation to model the spreading of a species, which is now known as the Fisher-KPP model. A striking feature of the model is that it predicts an asymptotic spreading speed (determined by an associated traveling wave solution). Such a phenomenon has been observed in many examples of species spreading in the real world, and was first rigorously proved by Aronson-Weinberger (1975), after which much further developments of the mathematical theory for propagation have been achieved along various lines. In this talk, I will focus on one aspect of some recent developments of this theory, which involves reaction-diffusion equations with free boundaries. I will discuss the longtime dynamics of these models and the associated regularity questions, including some success stories and challenges. |
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