講座主題：Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation
專家姓名：李宏偉
工作單位：山東師范大學數學與統計學院
講座時間：2024年12月07日10:00-11:00
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
We investigate the nonlocal-in-time Allen-Cahn equation (NiTACE), which incorporates a nonlocal operator in time with a finite nonlocal memory. Our objective is to examine the well-posedness of the NiTACE by establishing the maximal Lp regularity for the nonlocal-in-time parabolic equations with fractional power kernels. Furthermore, we derive a uniform energy bound by leveraging the positive definite property of kernel functions. We also develop an energy-stable time stepping scheme specifically designed for the NiTACE. Additionally, we analyze the discrete maximum principle and energy dissipation law, which hold significant importance for phase field models. To ensure convergence, we verify the asymptotic compatibility of the proposed stable scheme. Lastly, we provide several numerical examples to illustrate the accuracy and effectiveness of our method.
主講人介紹：
李宏偉，山東師范大學數學與統計學院副教授。2012年獲香港浸會大學博士學位，2016-2017年獲國家留學基金委資助赴美國南卡羅來納大學進行學術交流。目前主要從事相場模型和無界區域上偏微分方程數值解法的研究工作。近年來先后主持國家自然科學基金、山東省自然科學基金4項，在JSC, JCAM, PRE等雜志上發表論文多篇。
