Wave breaking for a shallow water equation
type: Item
instance of: scholarly article
title: Wave breaking for a shallow water equation
zbMATH Open document ID: 1106.35070
author: Yong Zhou
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-04T00:00:00Z
review text: The author studies the shallow water equation \[ u_t- u_{xxt}+ 3uu_x= 2u_x u_{xx}+ uu_{xxx},\quad t> 0,\quad x\in\mathbb R, \] \[ u(x,0)= u_0(x),\qquad x\in \mathbb R, \] which can be considered as a bi-Hamiltonian generalization of Korteweg-de Vries equations. The wave is said to be broken, if the solution \(u\) remains bounded, but its slope becomes infinite in finite time. The author formulates three various sufficient conditions on initial data \(u_0(x)\) to guarantee the wave breaking. The conditions are written out as explicit integral or differential inequalities.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 2105764
MaRDI profile type: Publication
full work available at URL: j.na.2004.02.004
OpenAlex ID: W2048952452
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DOI: 10.1016/J.NA.2004.02.004
description: scientific article; zbMATH DE number 2105764