Helge Dietert


Welcome at my personal homepage. I am a Mathematician working on PDEs, which are motivated by physics and biology.

Picture of myself

My main focus are equations from kinetic theory and fluid dynamics. In kinetic theory, I am interested by the emergence of stability by the mixing of a transport operator (Landau damping) and the interaction with dissipation operators that are degenerate. A similar interplay can be found in fluid dynamics known as inviscid damping and enhanced dissipation. A fascinating interplay between the transport and diffusion can be observed for boundary layers where the interplay between the transport and (degenerate) diffusion leads to instability and ill-posedness.

Recently, I also started to work on cross-diffusion models which can share the entropy structure of kinetic theory. In such models, the possible instability by diffusion is well-known as Turing instability.

If you are curious about oscillators and synchronisation, I invite you to play with my interactive website.