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
Recent Publications of Prof. Dr. Marlies Pirner
$\bullet $ Marlies Pirner. A consistent non-linear Fokker-Planck model for a gas mixture of polyatomic molecules. arXiv e-prints, January 2025. arXiv:2501.04029.
$\bullet $ Marlies Pirner and Gayrat Toshpulatov. Hypocoercivity for the non-linear semiconductor Boltzmann equation. arXiv e-prints, November 2024. arXiv:2411.11023.
$\bullet $ Marlies Pirner. A consistent kinetic Fokker-Planck model for gas mixtures. Journal of Statistical Physics, 191(11):Paper No. 143, 18, October 2024. doi:10.1007/s10955-024-03361-1.
$\bullet $ Lena Baumann and Marlies Pirner. Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions. In Hyperbolic problems: theory, numerics, applications, HYP2022. Proceedings of the XVIII international conference, Málaga, Spain, June 20–24, 2022. Volume II, pages 259–270. Springer Nature Switzerland, 2024. doi:10.1007/978-3-031-55264-9_22.
$\bullet $ Marlies Pirner and Sandra Warnecke. A review on a general multi-species BGK model: Modelling, theory and numerics, pages 217–231. Springer Nature Singapore, September 2023. doi:10.1007/978-981-19-6462-6_17.
$\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 $ T. Herzing, C. Klingenberg, and M. Pirner. Hypocoercivity of the linearized BGK equation with stochastic coefficients. Methods and Applications of Analysis, 30(3):113–128, 2023. doi:10.4310/maa.2023.v30.n3.a2.
$\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, January 2023. doi:10.1016/j.jcp.2022.111729.
$\bullet $ Gianluca Favre, Marlies Pirner, and Christian Schmeiser. Thermalization of a rarefied gas with total energy conservation: Existence, hypocoercivity, macroscopic limit. Kinet. Relat. Mod., 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 Rep., 18(2):1047–1085, August 2022. doi:10.4171/owr/2021/19.
$\bullet $ Marlies Pirner. A review on BGK models for gas mixtures of mono and polyatomic molecules. Fluids, 6(11):393, November 2021. doi:10.3390/fluids6110393.
$\bullet $ J. Haack, C. Hauck, C. Klingenberg, M. Pirner, and S. Warnecke. A consistent BGK model with velocity-dependent collision frequency for gas mixtures. J. Stat. Phys., 184(3):Paper No. 31, 17, September 2021. doi:10.1007/s10955-021-02821-2.
$\bullet $ Gi-Chan Bae, Christian Klingenberg, Marlies Pirner, and Seok-Bae Yun. BGK model of the multi-species Uehling-Uhlenbeck equation. Kinet. Relat. Mod., 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. SIAM Multiscale Model. Simul., 18(2):970–998, May 2020. doi:10.1137/17M1141023.
$\bullet $ Christian Klingenberg, Marlies Pirner, and Gabriella Puppo. A consistent kinetic model for a two-component mixture of polyatomic molecules. Commun. Math. Sci., 17(1):149–173, May 2019. doi:10.4310/CMS.2019.v17.n1.a6.
$\bullet $ Liu Liu and Marlies Pirner. Hypocoercivity for a BGK model for gas mixtures. Journal of Differential Equations, 267(1):119–149, January 2019. doi:10.1016/j.jde.2019.01.006.