PDE Seminar: Parabolic nonstandard growth problems, André H. Erhardt, University of Oslo
Parabolic problems are often motivated by physical aspects. In particular, evolutionary equations and systems can be used to model physical processes as heat conduction or diffusion processes.
In my talk I will present certain parabolic problem related to electro-rheological fluids. Such fluids are of high technological interest, because of their ability to change the mechanical properties under the influence of exterior electro-magnetic field. Many electro-rheological fluids are suspensions consisting of solid particles and a carrier oil. These suspensions change their material properties dramatically if they are exposed to an electric field. I will present the modelling of such fluids, the existence, uniqueness and stability of weak solutions to such problems as well as certain regularity theory.