动理学及其相关方程研讨会

Workshop on kinetic and related equations

时间：2019年11月30日

地点：科技楼702

会议议程：

报告人：刘双乾（暨南大学）

报告题目：Global mild solutions of the Landau and non-cutoff Boltzmann equations

报告摘要：The motion of the particles in the dilute gas can be described by the Landau equation or the non-cutoff Boltzmann equation. It is known that it is very difficult to construct the global well-posedness in Sobolev space for the initial boundary value problems of the kinetic equations in general bounded domains due to the formation of singularity of solutions. In this talk, firstly, we will discuss how to establish the global existence in some sharp regularity space for both the Landau equation and the non-cutoff Boltzmann equation with either the inflow boundary condition or the specular reflection boundary condition in a finite channel, secondly, we will show the solutions tend to the equilibrium around a global Maxwellian with the time sub-exponential decay rates, thirdly, we will present the regularity of the initial data or boundary data can be propagated from the boundary into the interior of the channel along the tangential direction. This is partly joint work with R. Duan, S. Sakamoto and R. Strain.

报告人：张筑（香港城市大学）

报告题目：Instability in a Vlasov-Fokker-Planck binary mixture

报告摘要：This talk is concerned with a kinetic model of Vlasov-Fokker-Planck system used to describe the motion of the mixed two species particles interacting through a potential and a thermal reservior at a given temperature. We will show that, when the temperature is under the threshold, the constant-equilibrium states are unstable.

报告人：樊迎哲(南阳师范学院)

报告题目：The Boltzmann equation with frictional force for very soft potentials in the whole space

报告摘要: We develop a general energy method for proving the optimal time

decay rates of the higher-order spatial derivatives of solutions to the Boltzmann_type and Landau-type systems in the whole space, for both hard potentials and oft potentials. With the help of this method, we establish the global existence and temporal convergence rates of solution near a given global Maxwellian to the Cauchy problem on the Boltzmann equation with frictional force for very soft potentials i.e. 3 < γ < 2.

报告人：张光辉（申博sunbet官网）

报告题目：Asymptotic behavior of the principal eigenvalue of a linear elliptic operator with small/large diffusion

报告摘要：We are concerned with an eigenvalue problem of a second order linear elliptic operator complemented by a general boundary condition. We aim to investigate the asymptotic behavior of the principal eigenvalue as the diffusive coefficient goes to 0 or infinity.