Diffusive stability of spatially periodic solutions of the Brusselator model
Analysis of PDEs
2018-01-17 v1
Abstract
Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the canonical second-order system of reaction diffusion equations given by the Brusselator model. Our results confirm that stability is accurately predicted in the small-amplitude limit by the formal Ginzburg Landau amplitude equations, rigorously validating the standard weakly unstable approximation and Eckhaus criterion.
Keywords
Cite
@article{arxiv.1608.08476,
title = {Diffusive stability of spatially periodic solutions of the Brusselator model},
author = {Alim Sukhtayev and Kevin Zumbrun and Soyeun Jung and Raghavendra Venkatraman},
journal= {arXiv preprint arXiv:1608.08476},
year = {2018}
}