Numerical Analysis of equivariant evolution equations
Description
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.
Members
Preprints
