Periodic initial-value problem for BBM-equation
type: Item
instance of: scholarly article
title: Periodic initial-value problem for BBM-equation
zbMATH Open document ID: 1072.35573
author: Hongqiu Chen
publication date: 2005-05-12T00:00:00Z
review text: The BBM or regularized long-wave equation \[ u_t+u_x+uu_x-u_{xxt}=0,\;x\in\mathbb{R},\;t>0,\quad u(x,0)=\varphi(x),\;x\in\mathbb{R},\tag{1} \] was originally proposed as an alternative to the Korteweg-de Vries equation in describing small-amplitude, long surface wave propatation. Its well-posedness in \(H^1(\mathbb{R})\) and \(L_2(\mathbb{R})\) have been studied by many authors. We consider the BBM-equation while the initial data \(\varphi\) is a periodic function on \(\mathbb{R}\). The result is that if \(\varphi\) is Lebesgue measurable and square-integrable within one period interval, then equation (1) is globally well posed in time \(t\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 42A45
zbMATH DE Number: 2167473
zbMATH Keywords: Benjamin-Bona-Mahony equations
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.10.023
OpenAlex ID: W2057945049
cites work: Model equations for long waves in nonlinear dispersive systems
cites work: Long waves on a beach
cites work: Q4151274
DOI: 10.1016/J.CAMWA.2004.10.023
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 2167473