Main:With the supervision of Prof. Christian Schmeiser, I'm studying the long time behavior for kinetic problems. We are focusing on convergence to equilibrium problems, especially those involving hypocoercivity. Hypocoercivity is a strong tool to show exponential convergence to equilibrium with quantitative rates for spatially inhomogeneous kinetic equations.
- Hypocoercivity and fast reaction limit for linear reaction networks with kinetic transport
- Kinetic model with thermalization for a gas with energy conservation (with Marlies Pirner)
- Kinetic model describing the particles generation-recombination phenomenon (with Marlies Pirner)
- I am working with Franca Hoffmann on stability analysis for a kinetic bacterial chemotaxis model. We are trying to adapt the L^2 hypocoercivity approach [Dolbeault-Mouhot-Schmeiser] to the results obtained by Hoffmann and Calvez for the macrosopic case. Vincent Calvez is involved in this project too.
- In collaboration with Paul Stocker I worked on the numerics for a kinetic model describing thermalization where the energy exchange with the background is considered. In particular, the thermal and the kinetic energy are exchanged between the moving particles and the background. (A fancy simulation showing the local convergence of the velocity distribution towards the Maxwellian)
- Paul Stocker and me are collaborating with Prof. Karel Svadlenka at the University of Kyoto. The goal is to have a better understanding of the models based on interface networks describing the molecules adhesion.
- I also worked with Prof. Giulio Schimperna on existence and regularities results for coupled Navier-Stokes and Allen-Cahn systems.
Future projects (?):
- Opinion formation considerering ranked agents based on their global influence and popularity is a topic that I would understand better. Toghether with Marie-Therese Wolfram, we are trying to find an appropriate model for this problem.
- Modelling and long time behavior for a model describing particles interacting and exchanging energy with the background, i.e. kinetic reaction equation coupled with parabolic equation for the thermal energy and a third equation describing the evolution of the internal energy of each particle.
- Open to new problem :)