# Prosjekt- og masteroppgaver for Katrin Grunert

My research focuses on nonlinear partial differential equations that describe wave phenomena, e.g. wave breaking and shock formation. A common feature that these equations share is that solutions to some given initial data are no longer unique in general.

To some extend one can compare this to the ordinary differential equation \[\dot x(t)= \sqrt{\vert x(t)\vert },\quad x(0)=a, \quad (a\in\mathbb{R})\] not having a unique global solution. In fact there are infinitely many solutions to the above problem. Introducing some additional constraints one can single out a unique global solution.

To make a long story short possible projects can be

- characterising different types of unique (weak) solutions
- investigating the stability of such solutions
- investigating the regularity of solutions
- …

Recommended prerequisites (but not a must): Ordinary differential equations / Dynamical systems, Linear methods, Partial differential equations, Real analysis

OBS: I am far from being an expert in numerics, i.e. if you are interested in a project using numerics feel free to contact other WaNP members.

In case of interest, write an email or stop by my office.