报告人: 刘双乾

报告题目: The initial boundary value problem for the Boltzmann equation with soft potential

报告人简介: 刘双乾：教授，暨南大学数学系，2009年博士毕业于武汉大学，主要研究方向为动理学方程及相关模型的数学理论。近五年先后在Archive for Rational Mechanics and Analysis、Communications in Mathematical Physics、SIAM Journal on Mathematical Analysis、Journal of Functioal Analysis、Journal of Differential Equations、 Mathematical Models and Methods in Applied Sciences等国际主流数学杂志发表论文20余篇。

报告摘要：Boundary effects are central to the dynamics of the dilute particles governed by Boltzmann equation. In this talk, we will report some recent studies on both the diffuse reflection and the specular reflection boundary value problems for Boltzmann equation with soft potential. For the diffuse reflection boundary condition, we capture some new properties of the probability integrals along the stochastic cycles and improve the $L^2-L^∞$ theory to give a more direct approach to obtain the global existence and time decay rate.  As to the specular reflection condition, our key contribution is to develop a new time-velocity weighted $L^∞$ theory so that we could deal with the greater difficulties stemmed from the complicated velocity relations among the specular cycles and the zero lower bound of the collision frequency. These methods in the latter case can be applied to the Boltzmann equation with soft potential for all other types of boundary condition.

报告时间：2016年10月21日15:00-16:00

报告地点: 科技楼南楼702