Seminars

A mathematical model for a (nonlinear) Darcy process

Author:Vince Ervin    Publicsh date:2016-05-19    Clicks:540
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 conside ......
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.