講座主題：Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation
專(zhuān)家姓名：李宏偉
工作單位：山東師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
講座時(shí)間：2024年12月07日10:00-11:00
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室341
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：
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(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院副教授。2012年獲香港浸會(huì)大學(xué)博士學(xué)位，2016-2017年獲國(guó)家留學(xué)基金委資助赴美國(guó)南卡羅來(lái)納大學(xué)進(jìn)行學(xué)術(shù)交流。目前主要從事相場(chǎng)模型和無(wú)界區(qū)域上偏微分方程數(shù)值解法的研究工作。近年來(lái)先后主持國(guó)家自然科學(xué)基金、山東省自然科學(xué)基金4項(xiàng)，在JSC, JCAM, PRE等雜志上發(fā)表論文多篇。
