讲座主题：Spectral Petrov-Galerkin method for optimal control problem governed by nonlocal diffusion equations driven by additive fractional Brownian motion

专家姓名：曹婉容

工作单位：东南大学数学院

讲座时间：2024年06月28日10:30-12:00

讲座地点：数学院三楼338

主办单位：烟台大学数学与信息科学学院

内容摘要：

A spectral Petrov-Galerkin method is developed to solve an optimal control problem governed by a nonlocal diffusion-reaction equation with a two-sided fractional derivative operator and driven by an additive fractional Brownian motion. In order to compensate weak singularities of the solution near boundaries, regularity of the fractional noise is analyzed in weighted Sobolev space, and the regularity of optimal control problem is also given. The spectral Petrov-Garlerkin method is presented by employing truncated spectral expansion of the fractional Brownian motion (fBm) type noise, and error estimates are given based on the obtained regularity of the optimal control problem. Numerical experiments are carried out to verify the theoretical findings.

主讲人介绍：

曹婉容，东南大学数学学院，教授，博士生导师，博士毕业于哈尔滨工业大学数学系，长期从事微分方程数值解、随机计算、非线性及非局部模型高效算法及仿真方面的研究，在SIAM Journal on Scientific Computing，Journal of Scientific Computing, Journal of Computational and Applied Mathematics等国际主流计算数学期刊上发表论文50余篇。已主持完成和参与完成国家自然科学基金项目4项，目前主持在研国家自然科学基金面上项目1项。主讲《随机模型及计算》和研究生《数值分析》、《随机微分方程数值解》等课程，主持完成江苏省教改课题一项，获得东南大学研究生教学成果奖一项（排二）。