'The Japan Society for Industrial and Applied Mathematics'
Abstract
We consider the five-component Meinhardt-Gierer
model for mutually exclusive patterns and
segmentation. We
prove rigorous results on the existence and
stability of mutually exclusive spikes which are
located in different positions for the two
activators.
Sufficient conditions for existence and stability
are derived, which depend in particular on the
relative size of the various diffusion constants.
Our main analytical methods are the
Liapunov-Schmidt reduction
and nonlocal eigenvalue problems. The analytical
results are confirmed by numerical simulations
