校庆报告:
题目：Preservation of ergodicity in nonlinear evolution equations and its applications.
主讲人：Prof. Hiroshi Matano, （University of Tokyo, Japan）
时间：2008年11月6日下午3点-4点
地点：闵行校区数学楼102报告厅
Abstract:
A recurrent function is called ergodic if it has a certain averaging property. This concept is wider than and is often more natural than almost periodicity when one studies spatially heterogeneous behavior of solutions of nonlinear evolution equations. In this talk, I first present a rather simple general
principle that states that spatial ergodicity in the equation or in the initial data is inherited by the solutions. I will then apply this principle to front propagation in nonlinear diffusion equations and show that:
(1) travelling waves in spatially ergodic media have well-defined average speed;
(2) planar fronts in the spatially homogeneous Allen-Cahn equation are asymptotically stable under spatially ergodic perturbations.