题目：Generation and propagation of fine transition layers in the stochastic Allen-Cahn equation

报告人：Hiroshi Matano教授（东京大学）

时间：3月22日 下午3:30-4:30

地点：3号楼3楼报告厅

摘要：This talk is concerned with a stochastic Allen-Cahn equation in RN(N≥2) involving a small parameter ε and a "mild noise", which is a smooth random function of t that converges to white noise as the parameter ε→0.

We first show that steep transition layers --- or interfaces --- develop within a very short time, which we call the “generation of interface". Next we study the motion of those transition layers and derive a stochastic motion law for the sharp interface limit as ε→0.

Furthermore, we prove that the solution profile near the interface remains close to that of a (squeezed) travelling wave, which means that the presence of the noise does not destroy the solution profile near the interface so long as the noise is spatially uniform.

Our work gives the first rigorous result on the generation of interface for the stochastic Allen-Cahn equation. Our results on the motion of interface also improve the earlier results of Funaki (1999) and Weber (2010) by considerably weakening the requirements for the initial data and establishing the robustness of the solution profile near the interface that has not been known before.

This talk is based on my joint work with Matthieu Alfaro (Montpellier), Dimitra Antonopoulou (Chester) and Georgia Karali (Crete).

Hiroshi Matano教授简介

东京大学Hiroshi Matano教授是国际著名数学家，是国际公认的抛物方程领域的领导人之一。

1994年他受邀参加世界数学家大会（ICM，苏黎世）并做45分钟报告（那届，亚洲微分方程界只有他与北大张恭庆教授获此殊荣）。1990年他获得日本数学界最高奖 --- 春季奖。

Matano教授一直从事抛物方程的研究，在许多方面做出过里程碑式的贡献，这些工作包括：

l  他是单调动力系统理论的奠基人之一；

l  他给出的零点性质已经成为研究抛物方程定性理论的有力工具；

l  他将行波解概念推广到递归情形；

l  他对爆破解的研究曾获得突破性的进展。