日時：2021年7月29日 (木)　16:00〜17:00
講演者：Dongyuan Xiao (Univ. of Montpellier・IMAG）

講演題目 ：Lotka-Volterra competition-diffusion system: the critical case

アブストラクト
We consider the reaction-diffusion competition system u_t=u_{xx}+u(1-u-v), v_t=dv_{xx}+rv(1-v-u), which is the so-called critical case. The associated ODE system then admits infinitely many equilibria, which makes the analysis quite intricate. We first prove the non-existence of monotone traveling waves by applying the phase plane analysis. Next, we study the long time behavior of the solution of the Cauchy problem with a compactly
supported initial datum. We not only reveal that the ''faster'' species excludes the  ''slower'' species (with an identified ''spreading speed''), but also provide a sharp description of the profile of the solution, thus shedding light on a new ''bump phenomenon''.