| Abstract: |
| In this talk, we present a joint work with O. Tough on the existence and uniqueness of positive bounded stationary solutions to the Fisher-KPP equation in unbounded domains, with Dirichlet boundary conditions. Under strong KPP-type assumptions, we derive a necessary and sufficient condition for existence in dimensions $\leq 6$, expressed in terms of the generalized principal eigenvalue. We further show that, whenever it exists, the solution is unique. As an application, one infers that for branching Brownian motion, global survival implies local survival in low dimensions. |
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