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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2016

Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation

Résumé

We prove the multidimensional stability of planar traveling waves for scalar nonlocal Allen-Cahn equations using semigroup estimates. We show that if the traveling wave is spectrally stable in one space dimension, then it is stable in n-space dimension, n ≥ 2, with perturbations of the traveling wave decaying like t −(n−1)/4 as t → +∞ in H k (R n) for k ≥ n+1 2 .
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Dates et versions

hal-01682322 , version 1 (12-01-2018)

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Grégory Faye. Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation. Discrete and Continuous Dynamical Systems - Series A, 2016, 36 (5), pp.2473 - 2496. ⟨10.3934/dcds.2016.36.2473⟩. ⟨hal-01682322⟩
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