讲座主题：Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation

专家姓名：李宏伟

工作单位：山东师范大学数学与统计学院

讲座时间：2024年12月07日10:00-11:00

讲座地点：数学院大会议室341

主办单位：tyc1286太阳集团数学与信息科学学院

内容摘要：

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.

主讲人介绍：

李宏伟，山东师范大学数学与统计学院副教授。2012年获香港浸会大学博士学位，2016-2017年获国家留学基金委资助赴美国南卡罗来纳大学进行学术交流。目前主要从事相场模型和无界区域上偏微分方程数值解法的研究工作。近年来先后主持国家自然科学基金、山东省自然科学基金4项，在JSC, JCAM, PRE等杂志上发表论文多篇。