Christian Klingenberg

research interests:

Mathematical Fluid Mechanics

theory of hyperbolic conservation laws

• towards a proper solution concept for the multi-dim. compressible Euler equations

• convex integration, non-uniqueness for the multi-dim. compressible Euler equations

structure preserving numerical schemes for Euler and ideal magnetohydrodynamics

• well-balanced and low Mach schemes for Euler equations with gravity

• genuinely multi-dim. schemes

• structure-preserving compact high-order method method

applications in astrophysics

• numerical schemes for evolving stellar structure and evolution

• simulations of the evolution of the universe including magnetic fields

kinetic equations and plasma, theory & numerics

• multi-species models, existence and qualitative behavior

• numerical schemes for multi-species BGK equations based on a variational procedure

PDE inverse problems, kinetic models in biology with coefficients determined by experimental data

• theory: proving that it is possible to solve certain kinetic PDE inverse problems

• numerics: schemes that determine the coefficients from given experimental data

Our logo, showing the interplay between astrophysics (Cassiopeia) and fluid mechanics.

designed together with Sebastian Ohlmann

former workshops, conferences etc.:

- Seminar series from Sept. 2020 - May 2022 Hyperbolic equations: Structure preserving numerical methods and other topics, see here

- Oberwolfach workshop "Structure preserving numerical methods for hyperbolic equations", April 11 - 15, 2022 see here

- Oberwolfach workshop "Modelling phenomena from nature by hyperbolci conservation laws", April 11, 17, 2021 see here

- Fall school Oct. 1 - 5, 2018 in Würzburg: Hyperbolic conservation laws and mathematics of fluid mechanics, with lectures by Constantine Dafermos, Eduard Feireisl, Sara Daneri and Simon Markfelder

- 16th International Conference on Hyperbolic Problems, organized by M. Westdickenberg and myself Aug. 1 - 5, 2016.

- Workshop in Würzburg, June 30 - July 3, 2015, “Evolutionary Equations, theory & numerics”, see here

Dept. of Mathematics

Würzburg University

Emil Fischer Str. 40

97074 Würzburg

Germany

I am in room 03.011 (top floor)

phone: (0049) (0)931 318 5045

email: klingen "at" mathematik.uni-wuerzburg.de

upcoming visitors:

- Carlos Pares (Malaga, Spain), January 15 - 21, 2024

- Philippe Helluy (Straßburg), for a week in Feb. 18 - 24, 2024