Positive entropic schemes for a nonlinear fourth-order parabolic equation

José A. Carrillo; Ansgar Jüngel; Shaoqiang Tang

doi:10.3934/dcdsb.2003.3.1

Article Contents

2003, Volume 3, Issue 1: 1-20. Doi: 10.3934/dcdsb.2003.3.1

This issue Previous Article Next Article Instability of planar traveling waves in bistable reaction-diffusion systems

Positive entropic schemes for a nonlinear fourth-order parabolic equation

1.
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada
2.
Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz
3.
LTCS, Department of Mechanics and Engineering Science, Peking University, Beijing 100871

Received: February 28, 2002

Revised: June 30, 2002

Published: January 2003

Abstract Related Papers Cited by

Abstract

A finite-difference scheme with positivity-preserving and entropy-decreasing properties for a nonlinear fourth-order parabolic equation arising in quantum systems and interface fluctuations is derived. Initial-boundary value problems, the Cauchy problem and a rescaled equation are discussed. Based on this scheme we elucidate properties of the long-time asymptotics for this equation.

Keywords:

Finite difference method,
discrete positive solutions,
discrete entropy estimates,
long-time behavior of discrete solutions.

Mathematics Subject Classification: 65M06, 35G25.

Citation:

Article Metrics

HTML views() PDF downloads(79) Cited by(0)

Positive entropic schemes for a nonlinear fourth-order parabolic equation

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Positive entropic schemes for a nonlinear fourth-order parabolic equation

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content