Diffusive stability of oscillations in reaction-diffusion systems
| dc.creator | Gallay, Thierry | |
| dc.creator | Scheel, Arnd | |
| dc.date | 2008-06-30 | |
| dc.date.accessioned | 2026-07-07T09:47:29Z | |
| dc.date.available | 2026-07-07T09:47:29Z | |
| dc.description | 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. | |
| dc.description | 29 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/0806.4915 | |
| dc.identifier | http://arxiv.org/abs/0806.4915 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163894 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K57; 35B10; 35B35; 35B40 | |
| dc.title | Diffusive stability of oscillations in reaction-diffusion systems | |
| dc.type | text |