A variational approach to the stationary solutions of the Burgers equation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1257.35004
DOI: 10.1137/100804401
author: Lorenzo Bertini
author: Marcello Ponsiglione
published in: SIAM Journal on Mathematical Analysis
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1008.0550
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 82B24
zbMATH DE Number: 6070865
zbMATH Keywords: quasi-potential
zbMATH Keywords: \(\Gamma\)-convergence
zbMATH Keywords: one space dimension
zbMATH Keywords: inhomogeneous Dirichlet problem
zbMATH Keywords: viscous Burgers equation
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: standing wave solution
zbMATH Keywords: one-parameter family of minimizers
MaRDI profile type: Publication
OpenAlex ID: W2029367074
arXiv ID: 1008.0550
title: A variational approach to the stationary solutions of the Burgers equation
review text: The authors consider the inhomogeneous Dirichlet problem for the viscous Burgers equation on a bounded interval as the length of the interval tends to infinity. The problem possesses certain Lyapunov functional, whose minimizer is a unique stationary solution. It is studied the behavior of the functional in the limit of infinite interval length. A special attention is paid to the case when the boundary data correspond to a standing wave solution on the whole line. In this case the limiting functional possesses a one-parameter family of minimizers, and the sharp asymptotic cost corresponding to a given shift of the stationary solution is calculated.
description: scientific article; zbMATH DE number 6070865