Existence of travelling-wave solutions and local well-posedness of the Fowler equation

Borys Alvarez-Samaniego (1) , Pascal Azerad (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We study the existence of travelling-waves and local well-posedness in a subspace of $C_b^1(\mathbb{R})$ for a nonlinear evolution equation recently proposed by Andrew C. Fowler to study the dynamics of dunes.

Mots clés: travelling-wave; Nonlocal evolution equation; travelling-wave.

Domaines: Equations aux dérivées partielles [math.AP]

Borys Alvarez-Samaniego, Pascal Azerad. Existence of travelling-wave solutions and local well-posedness of the Fowler equation. Discrete and Continuous Dynamical Systems - Series B, 2009, 12 (04), pp.671 - 692. ⟨10.3934/dcdsb.2009.12.671⟩. ⟨hal-00257423v3⟩