| Abstract: |
| The Fisher KPP equation is closely connected to Branching Brownian Motion, through the McKean representation, its solution describes the distribution of the maximal particle in the branching system. In this talk, I will discuss the long time behavior of coupled Fisher KPP reaction diffusion systems with interacting components associated with multitype Branching Brownian Motion. For a two component system, we show that the interaction modifies the classical Bramson logarithmic delay. Our PDE approach confirms previously known probabilistic results and extends them to general Fisher KPP nonlinearities. More generally, for cascading systems with k components, we establish sharp front asymptotics and convergence to the minimal speed traveling wave, providing a PDE proof of the conjectured asymptotics for the median position of the maximal particle in a cascading Branching Brownian Motion. |
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