Diffusive stability of spatially periodic patterns with a conservation law
Analysis of PDEs
2016-10-25 v2
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 model introduced by Matthews and Cox for pattern formation with a conservation law. Our results confirm that stability is accurately predicted in the small-amplitude limit by the formal modified Ginzburg-Lanadau system (mGL) consisting of a coupled Ginzburg-Landau equation and mean mode equation derived by Matthews and Cox, rigorously validating the standard weakly unstable approximation.
Cite
@article{arxiv.1610.05395,
title = {Diffusive stability of spatially periodic patterns with a conservation law},
author = {Alim Sukhtayev},
journal= {arXiv preprint arXiv:1610.05395},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1608.08476