报告人1：Vince Ervin（Clemson University）

时间：5月19日（周四）下午2：00 ~3：00

地点：数学中心813

题目：A mathematical model for a (nonlinear) Darcy process

摘要：In this presentation we will consider a filtration process governed by the Darcy fluid flow equations, coupled with an equation for the changing porosity (permeability) of the medium. Of particular interest is to determine a ``reasonable'' mathematical model which permits a solution for the fluid velocity and pressure in the H_{div} and L^{2} spaces, respectively.

报告人2：Li Xiaofan（Illinois Institute of Technology）

时间：5月19日（周四）下午3：10 ~ 4：10

地点：数学中心813

题目：Numerical schemes for integro-differential equations related to alpha-stable processes

摘要：The mean first exit time, escape probability and transitional probability density are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, $\alpha$-stable type L\'evy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker-Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is shown to satisfy a discrete maximum principle and to be convergent. The numerical results for two prototypical stochastic systems, the Ornstein-Uhlenbeck system and the double-well system are shown.