报告题目 (Title)：Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise （具有分数阶积分可加性噪声的随机半线性分数分数阶次扩散的Galerkin有限元逼近）
报告人 (Speaker)：闫玉斌 教授（University of Chester, UK）
报告时间 (Time)：2023年4月26日(周三) 15：30-16：30
报告地点 (Place)：腾讯会议606-795-915
邀请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
报告摘要：A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order $ \alpha \in (0, 1)$, driven by fractionally integrated additive noise. After discussing the existence, uniqueness and regularity results, we approximate the noise with the piecewise constant function in time in order to obtain a regularized stochastic fractional subdiffusion problem. The regularized problem is then approximated by using the finite element method in spatial direction. The mean squared errors are proved based on the sharp estimates of the various Mittag-Leffler functions involved in the integrals. Numerical experiments are conducted to show that the numerical results are consistent with the theoretical findings. This is a joint work with Prof. Amiya Pani, IIT Bombay, India.
