学术活动

On rate of convergence to equilibrium for the Space homogeneous Boltzmann equation with angular cut-off

作者:   来源:  时间:2015-10-15

  题目:On rate of convergence to equilibrium for the Space homogeneous Boltzmann equation with angular cut-off

  报告人:卢旭光 教授(清华大学)

  摘要:In this talk we begin with a short introduction to the derivation and fundamental results of the Boltzmann equation (including famous works of Lanford, DiPerna-Lions, Desvillettes-Villani, etc.). Then we focus on the space homogeneous Boltzmann equation with angular cut-off. Given a mass-energy conserved solution of the equation. We are interested in the rate of convergence of the solution to equilibrium as time tends to infinity. Our recent work (joint with E.A.Carlen $/&$ M.C.Carvalho(2009) and C.Mouhot(2015)) show that if the particle interaction potential is soft, then the convergence to equilibrium is at most algebraic and relies heavily on the decay speed of the energy tail of the initial datum so that the convergence rate can be arbitrarily slow. Whereas if the particle interaction potential is hard, then the convergence to equilibrium is always exponential and the convergence rate is essentially determined only by the spectral gap of the corresponding linearized collision operator, in particular it does not depend on any local behavior of the initial datum.

  时间:10月15日(周四)下午16:00-17:00

  地点:首都师大北一区文科楼 507 教室

  欢迎全体师生积极参加!