2020年05月01日 (金) 17:00 -- 18:00 （注：通常と終了時刻が異なります．）
Validity of formal asymptotic expansions for singularly perturbed competition-diffusion systems
We consider a two-species competition-diffusion system involving a small parameter $\varepsilon>0$ and discuss the validity of formal asymptotic expansions of solutions near the sharp interface limit $\varepsilon\approx0$. We assume that the corresponding ODE system has two stable equilibria. As in the scalar Allen-Cahn equation, it is known that the motion of the sharp interfaces of such systems is governed by a mean curvature flow. The formal expansion also suggests that the profile of the transition layers converges to that of a traveling wave solution as $\varepsilon\rightarrow0$. In this talk, we rigorously verify this latter ansatz for a large class of initial data.