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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2008

Qualitative properties of monostable pulsating fronts : exponential decay and monotonicity

Résumé

In this paper, we prove various qualitative properties of pulsating travelling fronts in periodic media, for reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov type or general monostable nonlinearities. Besides monotonicity, the main part of the paper is devoted to the exponential behavior of the fronts when they approch their unstable limiting state. In the general monostable case, the logarithmic equivalent of the fronts is shown and for noncritical speeds, the decay rate is the same as in the KPP case. These results also generalize the known results in the homogeneous case or in the case when the equation is invariant by translation along the direction of propagation.
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Dates et versions

hal-00174268 , version 1 (22-09-2007)

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  • HAL Id : hal-00174268 , version 1

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Francois Hamel. Qualitative properties of monostable pulsating fronts : exponential decay and monotonicity. Journal de Mathématiques Pures et Appliquées, 2008, pp.355. ⟨hal-00174268⟩
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