Research Group "Partial Differential Equations"

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Head:
Alexander Mielke

Coworkers:
Annegret Glitzky, Karoline Götze, Pascal Gussmann, Sebastian Heinz, Wolfgang Höppner, Hans-Christoph Kaiser, Thomas Koprucki, Matthias Liero, Hagen Neidhardt, Reiner Nürnberg, Florian Platzek, Paul Racec, Joachim Rehberg, Sina Reichelt, Marita Thomas, Lukas Wilhelm

Secretary:
Olga Kuphal

Honorary Members:
Herbert Gajewski, Konrad Gröger

Friedrich Wilhelm Bessel Awardee by Alexander von Humboldt Foundation:
Ulisse Stefanelli (IMATI-CNR, Italy)

Overview

Many fundamental processes in nature and technology can be described by partial differential equations and variational equations. The research group is working on the analytical theory of such equations (existence, uniqueness, qualitative behaviour) and on the development and implementation of algorithms for their numerical solution. The algorithms are used for the numerical simulation in industrial applications. The functionality of modern materials, for instance, relies on the complex interplay of effects on several length and time scales as well as on different physical effects, such as mechanics, thermodynamics, optics, and electromagnetism. The main topics of research are mathematical models of carrier transport in semiconductors and optoelectronic devices and reaction-diffusion equations for the transport of dopants in solids. Furthermore, nonlinear material models for linearized and nonlinear elasticity and plasticity as well as for systems with internal variables are under study. In this context, we develop in particular methods for multiscale problems.

The research group takes part in the following main application areas: