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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2023

Quantifying the threshold phenomena for propagation in nonlocal diffusion equations

Résumé

We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such phenomena. The outcomes dramatically depend on the tails of the dispersal kernel and can take a large variety of different forms. The strategy is to combine sharp estimates of the tails of the sum of i.i.d. random variables (coming, in particular, from large deviation theory) and the construction of accurate sub-and super-solutions.
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Dates et versions

hal-03509972 , version 1 (04-01-2022)

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Matthieu Alfaro, Arnaud Ducrot, Hao Kang. Quantifying the threshold phenomena for propagation in nonlocal diffusion equations. SIAM Journal on Mathematical Analysis, 2023, ⟨10.48550/arXiv.2201.01512⟩. ⟨hal-03509972⟩
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