1、赵会江报告题目：

Nonlinear Stability and Decay Rates toward Planar Boundary Layer Solutions for Damped Wave Equation with Large Initial Perturbation

报告时间：2010年12月3日下午3:00（星期五）

地    点：信息系会议室

赵会江教授个人简介

武汉大学数学与统计学院常务副院长，教授，博士生导师，

2000年入选中国科学院百人计划，

2009年获得国家杰出青年基金。

2、杨彤教授报告题目：

Well-posedness and qualitative properties for Boltzmann equation without angular cutoff

报告时间：2010年12月6日上午10:00（星期一）

地    点：信息系会议室

摘要: It is known that the singularity in the non-cutoff cross-section of the Boltzmann collision operator leads to the gain of regularity in the velocity variable. By defining and analyzing a new non-isotropic norm which precisely captures the dissipation in the linearized collision operator, we first give a precise coercive estimate for general physical cross-sections. Then the Cauchy problem for the Boltzmann equation is considered in the framework of small perturbation of an equilibrium state where  the global existence of classical solution is established in a general setting. With some essential estimates on the collision operators, the proof is based on the energy method through macro-micro decomposition. Furthermore, we study the qualitative properties of solutions, precisely, the full regularization in all variables, uniqueness, non-negativity and convergence rate to the equilibrium. The key step to obtain the regularizing effect is a generalized version of the uncertainty principle together with a theory of pseudo-differential calculus on non-linear collision operators. In summary, the above results lead to a satisfactory mathematical theory for the space inhomogeneous Boltzmann equation without angular cutoff.

杨彤教授个人简介

PhD in Mathematics, University of California, Davis，USA

香港城市大学科学和工程学院副院长，讲座教授，

“长江学者奖励计划”讲座教授，

国家杰出青年基金（B类），

晨兴数学奖银奖获得者。