After successful completion of the course, students are able to specify and apply a selection of PDE-applications in natural sciences and technology, and to discuss them from a mathematics perspective. They are able to describe the modelling assumptions or restrictions, as well as their essential analytical and numerical properties.

fluid dynamical models (Euler, Navier-Stokes, vortex models), traffic
flow models, theory of elasticity, hyperbolic conservation laws, image processing models (nonlinear diffusion filter, shock filter), models for pattern formation
(reaktion-diffusion equations, Turing instability), evolution of thin films, collective behavior (kinetic equations)

Derivation of PDE-models from basic physical principles, model simplifications

oral exam at the end of the semester

Lecture notes

Partial differential equations;

basic knowledge in physics / mechanics is helpful