Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 415921, 24 pages
http://dx.doi.org/10.1155/2011/415921
Research Article

Stability and Numerical Analysis of the Hébraud-Lequeux Model for Suspensions

Ángel Giménez,1 Francisco Morillas,2 José Valero,1 and José María Amigó1

1Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avenida. Universidad s/n, 03202 Elche (Alicante), Spain
2Departament d'Economia Aplicada, Facultat d'Economia, Universitat de València, Campus dels Tarongers s/n, 46022 València, Spain

Received 27 October 2010; Accepted 16 March 2011

Academic Editor: Miha'ly Pituk

Copyright © 2011 Ángel Giménez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study both analytically and numerically the stability of the solutions of the Hébraud-Lequeux equation. This parabolic equation models the evolution for the probability of finding a stress 𝜎 in a mesoscopic block of a concentrated suspension, a non-Newtonian fluid. We prove a new result concerning the stability of the fixed points of the equation, and pose some conjectures about stability, based on numerical evidence.