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

2020/10/07 by Guenther Hoermann, Hoermann, Guenther
Mathematics · Physics and Astronomy · #35B99 #35L65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2010.03257

openalex publication_date 2020/10/07 · openalex created_date 2020/10/15 · openalex updated_date 2026/07/28

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.

Citations

• Wave breaking for nonlinear nonlocal shallow water equations

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