English

Solution concepts, well-posedness, and wave breaking for the Fornberg-Whitham equation

Analysis of PDEs 2020-10-08 v1

Abstract

We discuss concepts and review results about the Cauchy problem for the Fornberg-Whitham equation, which has also been called Burgers-Poisson equation in the literature. Our focus is on a comparison of various strong and weak solution concepts as well as on blow-up of strong solutions in the form of wave breaking. Along the way we add aspects regarding semiboundedness at blow-up, from semigroups of nonlinear operators to the Cauchy problem, and about continuous traveling waves as weak solutions.

Keywords

Cite

@article{arxiv.2010.03257,
  title  = {Solution concepts, well-posedness, and wave breaking for the Fornberg-Whitham equation},
  author = {Guenther Hoermann},
  journal= {arXiv preprint arXiv:2010.03257},
  year   = {2020}
}