62 citations · 139 across the 25 of their papers we have counts for
26 papers
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…
Numerical schemes for a multi-species quantum BGK model
Gi-Chan Bae, Marlies Pirner, Sandra Warnecke
This work is devoted to the numerical implementation of the quantum Bhatnagar- Gross-Krook (BGK) model for gas mixtures consisting of classical and quantum particles (fermions, bos…
Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions
Lena Baumann, Marlies Pirner
This paper concerns the linear Landau damping for the two species Vlasov-Poisson system for ions and electrons near Penrose stable equilibria. The result is an extension of the res…
A review on a general multi-species BGK model: modelling, theory and numerics
Marlies Pirner, Sandra Warnecke
In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular we consider an appro…
Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency
Jeffrey Haack, Cory Hauck, Christian Klingenberg +2
We consider a kinetic description of a multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in t…
BGK model for multi-component gases near a global Maxwellian
Gi-Chan Bae, Christian Klingenberg, Marlies Pirner +1
In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in \cite{mixmodel} when the initial data is a…
A review on BGK models for gas mixtures of mono and polyatomic molecules
Marlies Pirner
We consider the socalled Bathnagar-Gross-Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisf…
A consistent BGK model with velocity-dependent collision frequency for gas mixtures
Jeff Haack, Cory Hauck, Christian Klingenberg +2
We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entro…
Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model
Gianluca Favre, Marlies Pirner, Christian Schmeiser
A reaction-kinetic model for a two-species gas mixture undergoing pair generation and recombination reactions is considered on a flat torus. For dominant scattering with a non-movi…
Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit
Gianluca Favre, Marlies Pirner, Christian Schmeiser
The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of…
Hypocoercivity of the linearized BGK-equation with stochastic coefficients
Tobias Herzing, Christian Klingenberg, Marlies Pirner
In this paper we study the effect of randomness on a linearized BGK-model in one dimension. We prove exponential decay rate to a global equilibrium. This decay rate can be proven t…
BGK model of the multi-species Uehling-Uhlenbeck equation
Gi-Chan Bae, Christian Klingenberg, Marlies Pirner +1
We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide a sufficient condition that guarantees the existence of equilibrium coefficients so that…
Hypocoercivity for a BGK model for gas mixtures
Liu Liu, Marlies Pirner
We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continu…
Kinetic ES-BGK models for a multi-component gas mixture
Christian Klingenberg, Marlies Pirner, Gabriella Puppo
We consider a multi component mixture of inert gas in the kinetic regime by assuming that the total number of particles of each species remains constant. In this article we shall i…
On quantifying uncertainties for the linearized BGK kinetic equation
C. Klingenberg, Q. Li, M. Pirner
We consider the linearized BGK equation and want to quantify uncertainties in the case of modelling errors. More specifically, we want to quantify the error produced if the pre-det…
A consistent kinetic model for a two-component mixture of polyatomic molecules
Christian Klingenberg, Marlies Pirner, Gabriella Puppo
We consider a multi component gas mixture with translational and internal energy degrees of freedom assuming that the number of particles of each species remains constant. We will…
Using a kinetic BGK model to determine transport coefficients of gas mixtures
Christian Klingenberg, Marlies Pirner
We consider a non reactive two component gas mixture. In a macroscopic description of a gas mixture we expect four physical coefficients characterizing the physical behaviour of th…
Existence and uniqueness of mild solutions for BGK models for gas mixtures of polyatomic molecules
Marlies Pirner
We consider two models for a two component gas mixture with translational and internal energy degrees of freedom described by a BGK approximation assuming that the number of partic…
A BGK model for gas mixtures of polyatomic molecules allowing for slow and fast relaxation of the temperatures
Marlies Pirner
Kinetic models for polyatomic gases have two temperatures for the two different types of degrees of freedom, the translational and the internal energy degrees of freedom. Therefore…
Existence, Uniqueness and Positivity of solutions for BGK models for mixtures
C. Klingenberg, M. Pirner
We consider kinetic models for a multi component gas mixture without chemical reactions. In the literature, one can find two types of BGK models in order to describe gas mixtures.…