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Research Interestshyperbolic partial differential equations, kinetic equations, Boltzmann equation, BGK approximation
long-time behavior of solutions, convergence to equilibrium
Existence, uniqueness of solutions
Qualitative behavior of solutions such as positivity of solutions, physical properties
Uncertainty quantification
Models considering gas mixtures, chemical reactions, degrees of freedom in internal energy, plasmas
Project membership
Mathematics Münster

C: Models and Approximations

C1: Evolution and asymptotics
Current PublicationsBae, Gi-Chan; Klingenberg, Christian; Pirner, Marlies; Yun, Seok-Bae BGK model for two-component gases near a global Maxwellian. SIAM Journal on Mathematical Analysis Vol. 55, 2023 online
Pirner, Marlies; Warnecke, Sandra A review on a general multi-species BGK model: modelling, theory and numerics. From Kinetik Theory to Turbulence Modeling, 2022 online
Favre, Gianluca; Pirner, Marlies; Schmeiser, Christian Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit. Kinetic and Related Models Vol. 15, 2022 online
Haack, Jeff; Hauck, Cory; Klingenberg, Christian; Pirner, Marlies; Warnecke, Sandra Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency. Journal of Computational Physics Vol. 473, 2022 online
Pirner, Marlies On multi-species BGK models with velocity dependent collision frequencies. Small Collaboration: Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations (hybridmeeting)Oberwolfach Report, 2021 online
Bae, Gi-Chan; Klingenberg, Christian; Pirner, Marlies; Yun, Seok-Bae BGK model of the multi-species Uehling Uhlenbeck equation. Kinetic and Related Models Vol. 14, 2021 online
Haack, Jeff; Hauck, Cory; Klingenberg, Christian; Pirner, Marlies; Warnecke, Sandra A consistent BGK model with velocity-dependent collision frequency for gas mixtures. Journal of Statistical Physics Vol. 184, 2021 online
Pirner, Marlies A review on BGK models for gas mixtures of mono and polyatomic molecules. Fluids Vol. 6, 2021 online
Crestetto, Anais; Klingenberg, Christian; Pirner, Marlies Kinetic/fluid micro-macro numerical scheme for a two component gas mixture. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Vol. 18, 2020 online
Current ProjectsEXC 2044 - C1: Evolution and asymptotics In this unit, we will use generalisations of optimal transport metrics to develop gradient flow descriptions of (cross)-diffusion-reaction systems, rigorously analyse their pattern forming properties, and develop corresponding efficient numerical schemes. Related transport-type- and hyperbolic systems will be compared with respect to their pattern-forming behaviour, especially when mass is conserved. Bifurcations and the effects of noise perturbations will be explored.

Moreover, we aim to understand defect structures, their stability and their interactions. Examples are the evolution of fractures in brittle materials and of vortices in fluids. Our analysis will explore the underlying geometry of defect dynamics such as gradient descents or Hamiltonian structures. Also, we will further develop continuum mechanics and asymptotic descriptions for multiple bodies which deform, divide, move, and dynamically attach to each other in order to better describe the bio-mechanics of growing and dividing soft tissues.

Finally, we are interested in the asymptotic analysis of various random structures as the size or the dimension of the structure goes to infinity. More specifically, we shall consider random polytopes and random trees.For random polytopes we would like to compute the expected number of faces in all dimensions, the expected (intrinsic) volume, and absorption probabilities, as well as higher moments and limit distributions for these quantities. online
E-Mailmarlies dot pirner at uni-muenster dot de
Phone+49 251 83-35088
FAX+49 251 83-32729
Secretary   Sekretariat Lückert
Frau Dr. Claudia Lückert
Telefon +49 251 83-35154
Fax +49 251 83-32729
Zimmer 120.025
AddressProf. Dr. Marlies Pirner
Angewandte Mathematik Münster: Institut für Analysis und Numerik
Fachbereich Mathematik und Informatik der Universität Münster
Orléans-Ring 10
48149 Münster
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