报告题目：On energy dissipation theory and numerical stability for time-fractional phase field equations
报 告 人：周涛，中国科学院数学与系统科学研究院
报告时间：2019年3月17日（星期日）上午8:30
报告地点：东校区机关楼316会议室
报告人简介：
周涛，中国科学院数学与系统科学研究院研究员，主要研究方向为不确定性定量化、正倒向随机微分方程数值解、谱方法等，有10余篇学术论文在Math. Comput.、SIAM J. Sci. Comput、J. Comput. Phys等计算数学顶级刊物上发表。现担任 Commun. Comput. Phys、 Int. J. Uncertainty Quantification、NMTMA等SCI期刊编委，主持国家自然科学基金面上项目，承担国家自然科学基金重大研究计划重点项目若干项。此外，周涛博士荣获中科院“陈景润未来之星”、“中国工业与应用数学学会优秀青年学者奖”等学术荣誉。
报告简介：
For the time-fractional phase field models, the corresponding energy dissipation law has not been well studied on both the continuous and the discrete levels. In this talk, we shall address this open issue. More precisely, we prove for the first time that the time-fractional phase field models indeed admit an energy dissipation law of an integral type. In the discrete level, we propose a class of finite difference schemes that can inherit the theoretical energy stability. Our discussion covers the time-fractional gradient systems, including the time-fractional Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional molecular beam epitaxy models. Numerical examples are presented to confirm the theoretical results. Moreover, a numerical study of the coarsening rate of random initial states depending on the fractional parameter $\alpha$ reveals that there are several coarsening stages for both the time-fractional Cahn-Hilliard equation and the time-fractional molecular beam epitaxy model, while there exists a $-\alpha/3$ power law coarsening stage. This is joint work with Prof. Tao Tang and Prof. Haijun Yu.
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