Doctoral Program
Dissipation and Dispersion
in Nonlinear PDEs

This Doctoral Program intends to provide a top-level scientific training of PhD students in the field of partial differential equations (including optimal transport), covering modeling, analysis, and numerics. The importance of partial differential equations (PDEs) comes from the fact that many questions for complex scientific and technical systems can be phrased in terms of differential equations. We focus the research exemplarily on dissipative and/or dispersive effects arising in PDEs.

Dissipation occurs in many modern applications, ranging from fluid dynamics and chemical kinetics to quantum semiconductors and collective human behavior. An important feature of dissipative dynamics is that the evolutionary system often approaches its global equilibrium exponentially fast. Dispersion occurs, for instance, in waves which interact with a medium, and it appears in water waves, transport in optical fibers, Bose-Einstein condensates, and even in human crowds. It may have regularizing effects, and for its understanding often novel mathematical techniques are needed. In many situations, dissipation and dispersion are strongly interconnected, like in ferromagnetic materials, quantum systems, fluid models, and wave-current interactions in surface water waves.

The first period of this Doctoral Program (DK) started in 2013 and is funded by the Austrian Science Fund FWF in association with the University of Vienna (Uni Wien) and the Vienna University of Technology (TU Wien). Intertwining a first-class training program and ambitious research projects, our long-term scientific goal is to contribute significantly to the comprehension of the interplay of dissipative-dispersive effects.