Research Interests
$\bullet$ hyperbolic partial differential equations, kinetic equations, Boltzmann equation, BGK approximation
$\bullet$ long-time behavior of solutions, convergence to equilibrium
$\bullet$ Existence, uniqueness of solutions
$\bullet$ Qualitative behavior of solutions such as positivity of solutions, physical properties
$\bullet$ Uncertainty quantification
$\bullet$ Models considering gas mixtures, chemical reactions, degrees of freedom in internal energy, plasmas
Current Cluster Publications of Prof. Dr. Marlies Pirner
$\bullet $ Marlies Pirner. A consistent kinetic fokker-planck model for gas mixtures. arXiv e-prints, March 2024. arXiv:2403.18478.
$\bullet $ Jeffrey Haack, Cory D. Hauck, Christian F. Klingenberg, Marlies Pirner, and Sandra Warnecke. Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency. Journal of Computational Physics, 473:Paper No. 111729, 29, November 2023. doi:10.1016/j.jcp.2022.111729.
$\bullet $ Gianluca Favre, Marlies Pirner, and Christian Schmeiser. Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model. Archive for Rational Mechanics and Analysis, 247(4):72, July 2023. doi:10.1007/s00205-023-01902-8.
$\bullet $ Gi-Chan Bae, Christian Klingenberg, Marlies Pirner, and Seok-Bae Yun. BGK model for two-component gases near a global Maxwellian. SIAM Journal on Mathematical Analysis, 55(2):1007–1047, April 2023. doi:10.1137/22M1469535.
$\bullet $ Lena Baumann and Marlies Pirner. Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions. arXiv e-prints, March 2023. arXiv:2303.14981.
$\bullet $ Gianluca Favre, Marlies Pirner, and Christian Schmeiser. Thermalization of a rarefied gas with total energy conservation: Existence, hypocoercivity, macroscopic limit. Kinetic and Related Models, 15(5):823–841, October 2022. doi:10.3934/krm.2022015.
$\bullet $ Christian Klingenberg, Qin Li, and Marlies Pirner. Small collaboration: modeling phenomena from nature by hyperbolic partial differential equations. Oberwolfach Reports, 18(2):1047–1085, August 2022. doi:10.4171/owr/2021/19.
$\bullet $ Gianluca Favre, Marlies Pirner, and Christian Schmeiser. Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model. arXiv e-prints, July 2022. doi:2012.15622.
$\bullet $ Marlies Pirner and Sandra Warnecke. A review on a general multi-species BGK model: Modelling, theory and numerics. arXiv e-prints, March 2022. arXiv:2203.15284.
$\bullet $ Gi-Chan Bae, Christian Klingenberg, Marlies Pirner, and Seok-Bae Yun. BGK model for multi-component gases near a global Maxwellian. arXiv e-prints, January 2022. arXiv:2201.01611.
$\bullet $ Marlies Pirner. A review on BGK models for gas mixtures of mono and polyatomic molecules. arXiv e-prints, October 2021. doi:2109.06005.
$\bullet $ J. Haack, C. Hauck, C. Klingenberg, M. Pirner, and S. Warnecke. A consistent BGK model with velocity-dependent collision frequency for gas mixtures. Journal of Statistical Physics, 184(3):Paper No. 31, 17, September 2021. doi:10.1007/s10955-021-02821-2.
$\bullet $ Tobias Herzing, Christian Klingenberg, and Marlies Pirner. Hypocoercivity of the linearized BGK-equation with stochastic coefficients. arXiv e-prints, May 2021. arXiv:2008.00322.
$\bullet $ Gi-Chan Bae, Christian Klingenberg, Marlies Pirner, and Seok-Bae Yun. BGK model of the multi-species Uehling-Uhlenbeck equation. Kinetic and Related Models, 14(1):25–44, February 2021. doi:10.3934/krm.2020047.
$\bullet $ Anaïs Crestetto, Christian Klingenberg, and Marlies Pirner. Kinetic/fluid micro-macro numerical scheme for a two component gas mixture. Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 18(2):970–998, May 2020. doi:10.1137/17M1141023.
$\bullet $ Liu Liu and Marlies Pirner. Hypocoercivity for a BGK model for gas mixtures. arXiv e-prints, January 2020. arXiv:1810.08590.
$\bullet $ Christian Klingenberg, Marlies Pirner, and Gabriella Puppo. A consistent kinetic model for a two-component mixture of polyatomic molecules. Communications in Mathematical Sciences, 17(1):149–173, May 2019. doi:10.4310/CMS.2019.v17.n1.a6.