Research

Research interests

• Ordinary and partial differential equations
• Dynamical systems, ergodic theory
• Kinetic theory, entropy methods
• Boltzmann equation and its BGK-type approximations, models for chemical reactions
• Long-time behaviour of solutions, convergence to equilibrium
• Physical applications

Current project participation

Modeling and mathematical description of concrete physical applications in the context of kinetic theory using the Bathnagar-Gross-Krook equation

Past project participation

Ergodic theory of nonlinear waves in discrete and continuous excitable media

Publications

• M. Keßeböhmer, J.D.M. Rademacher, D. Ulbrich.
  Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata.
  Ergodic Theory and Dynamical Systems. 2021;41(5):1397-1430 [DOI] | [arXiv]
• A. Pauthier, J.D.M. Rademacher, D. Ulbrich.
  Weak and strong interaction of excitation kinks in scalar parabolic equations.
  Journal of Dynamics and Differential Equations. Published: 30 July 2021; Volume 35, pages 2199-2235, (2023) [DOI] | [arXiv]

In progress:

• L. Liu, M. Pirner, D. Ulbrich.
  Discrete hypocoercivity for a nonlinear kinetic reaction model without initial close-to-equilibrium assumption. (working title)

Theses:

• D. Ulbrich.
  Ergodic theory of nonlinear waves in discrete and excitable excitable media.
  Dissertation, 2021 [DOI]