講座主題：Spectral Petrov-Galerkin method for optimal control problem governed by nonlocal diffusion equations driven by additive fractional Brownian motion
專家姓名：曹婉容
工作單位：東南大學(xué)數(shù)學(xué)院
講座時(shí)間：2024年06月28日10:30-12:00
講座地點(diǎn)：數(shù)學(xué)院三樓338
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
曹婉容，東南大學(xué)數(shù)學(xué)學(xué)院，教授，博士生導(dǎo)師，博士畢業(yè)于哈爾濱工業(yè)大學(xué)數(shù)學(xué)系，長期從事微分方程數(shù)值解、隨機(jī)計(jì)算、非線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等國際主流計(jì)算數(shù)學(xué)期刊上發(fā)表論文50余篇。已主持完成和參與完成國家自然科學(xué)基金項(xiàng)目4項(xiàng)，目前主持在研國家自然科學(xué)基金面上項(xiàng)目1項(xiàng)。主講《隨機(jī)模型及計(jì)算》和研究生《數(shù)值分析》、《隨機(jī)微分方程數(shù)值解》等課程，主持完成江蘇省教改課題一項(xiàng)，獲得東南大學(xué)研究生教學(xué)成果獎(jiǎng)一項(xiàng)（排二）。
