讲座论坛
On symmetry breaking of Allen-Cahn
发布时间:2021-11-05 14:43:36 314

演讲人Speaker:李栋讲席教授

题目Title:  On symmetry breaking of Allen-Cahn

时间Date:  2021年11月8日Time:10:00--11:00

地点Venue:T2栋 313

内容摘要Abstract:

This talk is concerned with numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computationalsolutions may converge  to completely incorrect steady states.  This happens for very smooth initial data and state-of-the-art algorithms. We analyze this phenomenon and showcase the resolution of this problem by a new symmetry-preserving filter technique. We develop a new theoretical framework and rigorously prove the convergence to steady states for the filtered solutions.

个人简介(About the speaker):

李栋,南方科技大学数学系讲席教授,国家特聘专家,主要从事偏微分方程和数值计算的理论研究,在Euler方程的不适定性问题、Kato-Ponce不等式、Skyrme模型Hedgehog解的全局稳定性,非局部运输方程的爆破理论和相场模型高精度算法稳定性分析等方面取得了一系列突破性的研究成果。他已在Inventiones Math, Duke, CPAM, JEMS, GAFA, SINUM 等国际重要数学刊物上发表学术论文100余篇。先后获得普林斯顿高等研究院Von Neumann Fellowship以及加拿大数学会Coxeter-James Prize等荣誉,于2017年当选香港Young Academy of Sciences创会会士。