The generalized Burgers equation with and without a time delay
type: Item
instance of: scholarly article
title: The generalized Burgers equation with and without a time delay
zbMATH Open document ID: 1071.35065
DOI: 10.1155/S1048953304210012
author: Nejib Smaoui
author: Mona M. Mekkaoui
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2005-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/51631
review text: The paper deals with the following generalized Burgers equation with time delay and periodic boundary condition \[ \begin{alignedat}{2} u_t(x,t) &= \nu u_{xx}(x,t) - u(x,t-\tau)u_x(x,t) + u(x,t), &\quad 0 &< x < 2\pi, \;t >0,\\ u(0,t) &= u(2\pi,t), &\quad t&>0,\\ u(x,s) &= u_0(x,s), &\quad 0&<x<2\pi, \;-\tau \leq s \leq 0. \end{alignedat} \] The authors show that the equation under consideration is exponentially stable under small delays. Using a pseudospectral method adequate numerical results are presented.
reviewed by: Emil Minchev
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 2161821
zbMATH Keywords: periodic boundary condition
zbMATH Keywords: pseudospectral method
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2161821