# Diffusive stability of oscillations in reaction-diffusion systems

Source: [Diffusive stability of oscillations in reaction-diffusion systems](<https://www.sota2.com/research/paper/68fa4de81e209131ce958397>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:09.052Z

Authors: Thierry Gallay, Arnd Scheel

Published: 2008-06-30T15:11:12.000Z

## Abstract

We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations decay algebraically with the diffusive rate t^{-n/2} in space dimension n. We also compute the leading order term in the asymptotic expansion of the solution, and show that it corresponds to a spatially localized modulation of the phase. Our approach is based on a normal form transformation in the kinetics ODE which partially decouples the phase equation, at the expense of making the whole system quasilinear. Stability is then obtained by a global fixed point argument in temporally weighted Sobolev spaces.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0806.4915>)

[PDF](<https://arxiv.org/pdf/0806.4915.pdf>)