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

Abstract

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.

arXiv comment21 pages

References in corpus (1)

• Breeding and Solitary Wave Behavior of Dunes

Cited by in corpus (6)

• Simultaneous denoising and enhancement of signals by a fractal conservation law
• Finite difference approximations for a fractional diffusion/anti-diffusion equation
• A non-monotone conservation law for dune morphodynamics
• Global-in-time existence of perturbations around travelling-waves
• Vanishing viscosity limit of a conservation law regularised by a Riesz-Feller operator
• Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem