報告人: 劉雙乾

報告題目: The initial boundary value problem for the Boltzmann equation with soft potential

報告人簡介: 劉雙乾：教授，暨南大學數學系，2009年博士畢業于武漢大學，主要研究方向為動理學方程及相關模型的數學理論。近五年先後在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等國際主流數學雜志發表論文20餘篇。

報告摘要：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.

報告時間：2016年10月21日15:00-16:00

報告地點: 科技樓南樓702