The project is devoted to spatial and temporal discretizations of gradient flows in Wasserstein-like metrics. The main examples under consideration are porous medium, thin film, and quantum drift diffusion equations. Our analysis is focussed on the inheritance of structural properties to the discretization, like the variational character of the dynamics, the monotonicity of the potential, the contractivity of the flow etc. In the third funding period, we shall mainly deal with flows that exhibit non-local effects, or that are given in non-genuine metric structures.
DFG Programme
CRC/Transregios
