Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project B3

## Numerical analysis of equivariant evolution equations

Principal Investigator(s) Other Investigators

## Summary:

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.

## Recent Preprints:

 17023 Semilinear Parabolic Differential Inclusions with One-sided Lipschitz Nonlinearities PDF | PS.GZ 17011 On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation PDF | PS.GZ 16043 Fredholm Properties and $L^p$-Spectra of Localized Rotating Waves in Parabolic Systems PDF | PS.GZ 16039 Freezing Traveling and Rotating Waves in Second Order Evolution Equations PDF | PS.GZ 16037 Computing stable hierarchies of fiber bundles PDF | PS.GZ 16022 Computation and Stability of Traveling Waves in Second Order Evolution Equations PDF | PS.GZ 16007 Spatial Decay of Rotating Waves in Reaction Diffusion Systems PDF | PS.GZ 15052 On the approximation of stable and unstable fiber bundles of (non)autonomous ODEs – a contour algorithm PDF | PS.GZ 15042 A new $L^p$-Antieigenvalue Condition for Ornstein-Uhlenbeck Operators PDF | PS.GZ 15030 Symbolic Coding for Noninvertible Systems: Uniform Approximation and Numerical Computation PDF | PS.GZ