Wave breaking and propagation speed for a class of one-dimensional shallow water equations
type: Item
instance of: scholarly article
title: Wave breaking and propagation speed for a class of one-dimensional shallow water equations
zbMATH Open document ID: 1230.35101
DOI: 10.1155/2011/647368
author: Zaihong Jiang
author: Sevdzhan Hakkaev
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: Summary: We investigate a more general family of one-dimensional shallow water equations. Analogous to the Camassa-Holm equation, these new equations admit blow-up phenomena and infinite propagation speed. First, we establish blow-up results for this family of equations under various classes of initial data. It turns out that it is the shape instead of the size and smoothness of the initial data which influences breakdown in finite time. Then, infinite propagation speed for the shallow water equations is proved in the following sense: the corresponding solution \(u(t, x)\) with compactly supported initial data \(u_0(x)\) does not have compact \(x\)-support any longer in its lifespan.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5997816
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/647368
OpenAlex ID: W2046367595
Wikidata QID: Q58654379
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description: scientific article; zbMATH DE number 5997816