On the instability of a nonlocal conservation law

Afaf Bouharguane

doi:10.3934/dcdss.2012.5.419

Article Contents

2012, Volume 5, Issue 3: 419-426. Doi: 10.3934/dcdss.2012.5.419

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On the instability of a nonlocal conservation law

Afaf Bouharguane^1,

1.
Institut de Mathématiques et de Modélisation de Monptellier, Université Montpellier II, 34 095 Montpellier

Received: August 2010

Revised: January 2011

Published: June 2012

Abstract / Introduction Related Papers Cited by

Abstract

We are interested in a nonlocal conservation law which describes the morphodynamics of sand dunes sheared by a fluid flow, recently proposed by Andrew C. Fowler and studied by [1,2]. We prove that constant solutions of Fowler's equation are non-linearly unstable. We also illustrate this fact using a finite difference scheme.

Keywords:

Mathematics Subject Classification: 35L65, 45K05, 35G25, 35C07, 35B35, 65M06.

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References

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