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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa Année : 2020

Interplay of nonlinear diffusion, initial tails and Allee effect on the speed of invasions

Thomas Giletti

Résumé

We focus on the spreading properties of solutions of monostable equations with non-linear diffusion. We consider both the porous medium diffusion and the fast diffusion regimes. Initial data may have heavy tails, which tends to accelerate the invasion phenomenon. On the other hand, the nonlinearity may involve a weak Allee effect, which tends to slow down the process. We study the balance between these three effects (nonlin-ear diffusion, initial tail, KPP nonlinearity/Allee effect), revealing the separation between " no acceleration " and " acceleration ". In most of the cases where acceleration occurs, we also give an accurate estimate of the position of the level sets.
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Dates et versions

hal-01646259 , version 1 (23-11-2017)
hal-01646259 , version 2 (26-08-2022)

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Matthieu Alfaro, Thomas Giletti. Interplay of nonlinear diffusion, initial tails and Allee effect on the speed of invasions. Annali della Scuola Normale Superiore di Pisa, 2020, XXI, pp.1223-1255. ⟨10.2422/2036-2145.201711_010⟩. ⟨hal-01646259v1⟩
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