Project: SFB 701: Spectral Structures and Topological Methods in Mathematics - Project B3

Numerical Analysis of equivariant evolution equations


The goal of the project is to develop and analyse numerical methods for computing moving patterns in time dependent partial differential equations. Examples are traveling waves in one, spiral waves in two, and scroll waves in three space dimensions. These occur in reaction diffusion systems and (non) viscous conservation laws that are equivariant with respect to the action of a Lie group. Our focus is the {\it freezing method\/} that allows to compute adaptive coordinate frames in which patterns become stationary. We investigate nonlinear stability of patterns, its relation to spectral properties, the influence of random perturbations, and we extend the method to handle multiple patterns.