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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2011

Diffusive stability of oscillations in reaction-diffusion systems

Thierry Gallay
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Résumé

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.
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Dates et versions

hal-00295164 , version 1 (11-11-2015)

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Thierry Gallay, Arnd Scheel. Diffusive stability of oscillations in reaction-diffusion systems. Transactions of the American Mathematical Society, 2011, 363 (5), pp.2571-2598. ⟨10.1090/S0002-9947-2010-05148-7⟩. ⟨hal-00295164⟩
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