Mathematics is a key discipline for today’s research landscape. It provides a language that makes it possible to describe and quantify complex processes in the natural and engineering sciences. Many achievements and amenities of modern life would not have been possible without mathematics. The mathematical analysis of applied models not only drives progress within the discipline itself, but also has the potential to impact applications in ways that cannot be predicted a priori.
The Research Training Group Energy, Entropy, and Dissipative Dynamics combines analysis, modeling, and numerics of nonlinear partial differential equations coming from physics, materials science, and geometry. A common theme among the research projects is the use of energy and entropy functionals and their dissipation mechanisms as a tool for the investigation of the qualitative and quantitative behavior of solutions.
Important topics include energy minimization, properties of energy landscapes, maximization of energy dissipation or entropy production as a selection criterion in time-dependent situations. The research projects focus on different applied models such as moment models in gas dynamics, hyperbolic conservation laws, kinetic partial differential equations, flows on networks, Landau-Lifshitz equations, and the models of geometric knot theory.