Global weak solutions and wave breaking phenomena to the periodic Degasperis-Procesi equation with strong dispersion
type: Item
instance of: scholarly article
title: Global weak solutions and wave breaking phenomena to the periodic Degasperis-Procesi equation with strong dispersion
zbMATH Open document ID: 1180.35162
author: Fei Guo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-10-09T00:00:00Z
review text: The author considers the initial value problem for the periodic Degasperis-Procesi equation with one spatial dimension. The DP-equation is a third-order dispersive conservation law. The dispersive term is assumed to be strong. Such problems appear as an approximation to the incompressible Euler equation for shallow water waves. The existence and uniqueness of the global weak solution are established. Periodic peakon and shock-peakon solutions are constructed. Moreover, two conservation laws (i.e. first integrals) are revealed.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 5612956
zbMATH Keywords: nonlinear third-order conservation laws
zbMATH Keywords: periodic initial-boundary problem
zbMATH Keywords: one spatial dimension
zbMATH Keywords: periodic peakon and shock-peakon
zbMATH Keywords: first integrals
MaRDI profile type: Publication
full work available at URL: j.na.2009.04.012
OpenAlex ID: W1971181155
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DOI: 10.1016/J.NA.2009.04.012
description: scientific article; zbMATH DE number 5612956