5 papers · 1 filter
Long time behavior of Fokker-Planck equations for bosons and fermions
Anton Arnold, Marlies Pirner, Gayrat Toshpulatov
This paper is concerned with space inhomogeneous quantum Fokker-Planck equations posed on a classical kinetic phase space. The nonlinear factor appears both in the tran…
BGK model for rarefied gas in a bounded domain
Hongxu Chen, Christian Klingenberg, Marlies Pirner
We study the Bathnagar-Gross-Krook (BGK) equation in a smooth bounded domain featuring a diffusive reflection boundary condition with general collision frequency. We prove that the…
A consistent non-linear Fokker-Planck model for a gas mixture of polyatomic molecules
Marlies Pirner
We consider a multi component gas mixture with translational and internal energy degrees of freedom without chemical reactions assuming that the number of particles of each species…
Hypocoercivity for the non-linear semiconductor Boltzmann equation
Marlies Pirner, Gayrat Toshpulatov
A kinetic model for semiconductor devices is considered on a flat torus. We prove exponential decay to equilibrium for this non-linear kinetic model by hypocoercivity estimates. Th…
A consistent kinetic Fokker-Planck model for gas mixtures
Marlies Pirner
We propose a general multi-species Fokker-Planck model. We prove consistency of our model: conservation properties, positivity of all temperatures, H-Theorem and the shape of equil…