On the instability of a nonlocal conservation law

Afaf Bouharguane (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We are interested in a nonlocal conservation law which describes the morphodynamics of sand dunes sheared by a fluid flow, recently proposed by Andrew C. Fowler. We prove that constant solutions of Fowler's equation are non-linearly unstable. We also illustrate this fact using a finite difference scheme.

Mots clés: instability; nonlocal evolution equation; fractional anti-diffusive operator; Duhamel formulation; instability.

Domaines: Equations aux dérivées partielles [math.AP]

Afaf Bouharguane. On the instability of a nonlocal conservation law. 2011. ⟨hal-00529766v2⟩