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Time-periodic solutions of the Vlasov-Poisson-Boltzmann system with a general external force in
Renjun Duan, Jinkai Ni
In this paper, we study the time-periodic problem for the Vlasov-Poisson-Boltzmann (VPB) system with a given time-periodic external force in the whole space . The for…
On a free boundary problem of the Boltzmann equation
Shengchuang Chang, Renjun Duan, Shuangqian Liu
This paper studies a free boundary problem for the Boltzmann equation that models the interaction of rarefied gas with a moving wall---a classical piston problem in kinetic theory.…
Half-space problem on the Boltzmann equation with zero Mach number at infinity
Hongxu Chen, Jun-ling Chen, Renjun Duan
We study the long-time dynamics of the time-evolutionary Boltzmann equation with hard sphere collisions in the three-dimensional half-space \( \mathbb{R}^2 \times \mathbb{R}^+\), s…
Three-dimensional time-periodic problem on the Boltzmann equation with external force
Renjun Duan, Jinkai Ni
The time-periodic problem for the Boltzmann equation with a prescribed time-periodic external force in the three-dimensional whole space has remained open since it was first treate…