Main:With Prof. Christian Schmeiser we study the long time behavior of system of particles described by kinetic equations. In particular convergence to equilibrium problems, 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)
- With Franca Hoffmann we are working 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 obtain from Hoffmann and Calvez for the macrosopic case. Vincent Calvez is involved to this project too.
- Togheter with Paul Stocker we did the numerics for a kinetic model describing thermalization where the enrgy 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)
- With Paul Stocker we 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 (?):
- Existence and regularity results for a cross diffusion system arising from the macroscopic limit of the kinetic model with exchange of energy studied with Schmeiser and Pirner.
- 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.
- Everything else :)