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arXiv · 1608.08476

Diffusive stability of spatially periodic solutions of the Brusselator model

Alim Sukhtayev·Kevin Zumbrun·Soyeun Jung·Raghavendra Venkatraman
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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.

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Alim Sukhtayev, Kevin Zumbrun, Soyeun Jung, Raghavendra Venkatraman. 2016-08-30. Diffusive stability of spatially periodic solutions of the Brusselator model. https://doi.org/10.1007/s00220-017-3056-x

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