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

TL;DR

This paper investigates the existence of travelling-wave solutions and establishes local well-posedness for a nonlinear evolution equation modeling dune dynamics, contributing to the mathematical understanding of such physical phenomena.

Contribution

It proves the existence of travelling-wave solutions and demonstrates local well-posedness in a specific function space for Fowler's dune evolution equation.

Findings

Existence of travelling-wave solutions confirmed.

Local well-posedness established in a subspace of $C_b^1( )$.

Mathematical framework for dune dynamics improved.

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.