学术报告报告题目：The sharp initial condition for existence and blow-up to some PDEs vs the best constant of functional inequalities
报 告 人：王金环教授(辽宁大学)
报告时间：2020年11 月10 日（星期二）下午14:00-15:00
报告地点：腾讯会议, 会议号：438103995
邀 请 人：金海洋 副教授
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数学学院
2020年11月9日
报告摘要：
In many physical and biological systems, there are some competing effects such as focus and de-focus, attraction and repulsion, spread and concentration. These competing effects usually are represented by terms with different signs in a free energy. The dynamics of the physical system sometimes can be described by a gradient ow driven by the free energy. Some functional inequalities can be used to determine the domination among these competing effects in the free energy, and provided sharp conditions on initial data or coefficients in the system for the global existence. In this talk, we will introduce some important relations between functional inequalities and sharp conditions for the global existence to seme PDE. For example, the Hardy-Littlewood-Sobolev inequality vs parabolic-elliptic Keller-Segel (K-S) model, Onofri's inequality vs linear parabolic-parabolic K-S model, Sobolev inequality vs degenerate parabolic-parabolic K-S model, and Sz. Nagy inequality vs 1-D thin film equation. And we prove global existence and blow-up of solutions for above models under sharp conditions. Moreover, we obtain the uniqueness of the weak solution for the linear diffusion Keller-Segel model using the refined hyper-contractivity of the Lp of the solution, and also obtain some results on the L1 estimate of the solution utilizing the bootstrap method.
报告人简介：
王金环，教授，博士生导师；现为辽宁大学数学院副院长。2009年大连理工大学博士毕业，2010-2012清华大学博士后，2014-2015美国Duke大学访问学者。 2015年入选辽宁省高校杰出青年学者成长计划，2017年入选辽宁省百千万人才“千层次”；现已在SIAM J. Math. Anal., Nonlinearity等国际重要期刊发表论文20余篇。已结题国家级项目3项，省级项目1项；在研省人才项目1项，省重点项目1项。