| Abstract: |
| In this paper we consider a non-local bistable reaction-diffusion equation arising from cell polarization. A typical solution of this model exhibits an interface with velocity regulated by the total mass. The feedback between mass-conservation and bistablity causes the interface to approach a fixed limit. In the limit of a small diffusivity $\epsilon^2 \ll 1$, we prove that the interface can be estimated within $O(\epsilon^\gamma)$ of the location as predicted using formal asymptotics, for any $\gamma$ less than 1/2. This is joint work with D. Gomez and Y. Mori at University of Pennsylvania. |
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