On the decay of step for the Korteweg-de Vries-Burgers equation
type: Item
instance of: scholarly article
title: On the decay of step for the Korteweg-de Vries-Burgers equation
zbMATH Open document ID: 0795.35109
DOI: 10.1007/BF01075285
author: Pavel I. Naumkin
author: I. A. Shishmarev
publication date: 1994-04-12T00:00:00Z
review text: We study the behavior, as \(t\to\infty\), of the solution \(u(x,t)\) of the Cauchy problem for \[ u_ t+ 2uu_ x+ au_{xxx}- u_{xx}=0 \] in the case \(| a|>1/8\). We prove that the solution \(u(x,t)\) converges to the stationary wave \(\varphi(x)\) as \(t\to\infty\) uniformly with respect to \(x\in \mathbb{R}\) in the case \(| a|>1/8\), and we obtain an estimate for the rate of convergence. Thus, the stationary wave is also asymptotically stable in the case \(| a|>1/8\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 525657
zbMATH Keywords: Cauchy problem
zbMATH Keywords: stationary wave
zbMATH Keywords: asymptotically stable
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01075285
OpenAlex ID: W1987400313
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 525657