Stability of fronts and transient behaviour in KPP systems

Stability of fronts and transient behaviour in KPP systems

We consider a system of two reaction diffusion equations with the Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearity which describes propagation of pressure-driven flames. It is known that the system admits a family of travelling wave solutions parameterized by their velocity. In this paper, we s...

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Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2010-06, Vol.466 (2118), p.1769-1788
Hauptverfasser: Ghazaryan, Anna, Gordon, Peter, Virodov, Alexander
Format: Artikel
Sprache:eng
Schlagworte:
Burn rate
Critical velocity
Flame propagation
Kolmogorov-Petrovsky-Piskunov (KPP) systems
Linearization
Mathematics
Meta-Stable Regimes
Nonlinearity
Phase velocity
Porous materials
Scalars
Speed
Stability
Travelling Fronts
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Beschreibung
Zusammenfassung:We consider a system of two reaction diffusion equations with the Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearity which describes propagation of pressure-driven flames. It is known that the system admits a family of travelling wave solutions parameterized by their velocity. In this paper, we show that these travelling fronts are stable under the assumption that perturbations belong to an appropriate weighted L2 space. We also discuss an interesting meta-stable pattern the system exhibits in certain cases.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2009.0400