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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