Convergence of a semidiscrete scheme for a forward-backward parabolic equation
type: Item
instance of: scholarly article
title: Convergence of a semidiscrete scheme for a forward-backward parabolic equation
zbMATH Open document ID: 1307.65118
author: Giovanni Bellettini
author: Carina Geldhauser
author: M. Novaga
published in: Advances in Differential Equations
publication date: 2013-05-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ade/1363266255
review text: The authors investigate the convergence of a semi-discrete scheme for the forward-backward parabolic equation \(u_t=(W'(u_x))_x\) with periodic boundary conditions in one space dimension, where \(W\) is a standard double-well potential. The authors characterize the equation satisfied by the limit of the discretized solutions as the grid size goes to zero. By an approximation argument, they prove that it is possible to flow initial data \(\overline{u}\) having regions where \(\overline{u}\) falls within the concave region \({W''<0}\) of \(W,\) where the backward character of the equation manifests itself. It is proved that the limit equation depends on the way one approximates \(\overline{u}\) in its unstable region.
reviewed by: Yasar Sozen
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65M20
zbMATH DE Number: 6166939
zbMATH Keywords: forward-backward barabolic equation
zbMATH Keywords: convergence
zbMATH Keywords: semidiscretization
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6166939