学术报告

题      目：Stability of viscous shocks for Burgers equations with fast diffusion and singularity

报  告  人：梅茗   教授  (邀请人：李颖花 )

                                     McGill University & Champlain College

时      间：5月24日  16：30-17：30

地     点：数科院东楼401

报告人简介:

       梅茗教授为加拿大尚布兰学院数学系的终身教授及加拿大麦吉尔大学数学与统计系的Adjunct Professor，同时也是东北师范大学的“长白山学者”讲座教授和“东师学者”讲座教授，以及日本金泽大学的合作教授。在流体力学中可压缩Navier-Stokes方程、Euler方程、Euler-Poisson方程、非线性波的稳定性、音速边界半导体动力学模型的数学分析等方面取得了系列重要的原创结果。其研究课题连续得到加拿大自然科学基金，加拿大魁北克省自然科学基金及魁北克省大专院校国际局的资助。在本领域的一流学术刊物Arch. Ration. Mech. Anal., SIAM J. Math. Anal.等发表论文 120 余篇。同时也是《Applicable Analysis》等5个SCI期刊的副主编和编委。

摘      要：

       In this talk, we present our recent studies on the stability of viscous shocks to Burgers equations with fast diffusion and singularity. When the constant state u+=0, Burgers equations possess a strong singularity due to the fast diffusion in porous media. In order to overcome this singularity, we adopt the technical weighted-energy method, where the weights are carefully selected, which are related to the viscous shocks. A number of numerical simulations are also carried out, which show that the shape of solution becomes steeper as the effect of fast diffusion is more strong.

      欢迎老师、同学们参加、交流！