| Abstract: |
| Threshold phenomena are a basic feature of bistable reaction-diffusion equations. They refer to the existence of critical initial data separating extinction from invasion, with convergence to a ground state at the threshold. I will first discuss the classical local case $\partial_t u = \partial_{xx} u + f(u)$, with emphasis on the role of the amplitude and the spatial arrangement of the initial condition, in particular through fragmentation effects. I will then turn to a nonlocal equation of the form $\partial_t u = \partial_{xx} u + r(x) u - u \int_{\mathbb{R}} u - h(u)$, where the threshold structure appears to be richer and may involve two distinct thresholds. |
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