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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 506863, 12 pages
http://dx.doi.org/10.5402/2012/506863
Research Article

Systems of Sticky Particles Governed by Burgers' Equation

DΓ©partement de MathΓ©matiques et Informatique, FacultΓ© des Sciences, UniversitΓ© des Sciences et Techniques de Masuku, BP 943 Franceville, Gabon

Received 20 October 2011; Accepted 28 November 2011

Academic Editor: G. F. Torres del Castillo

Copyright © 2012 Octave Moutsinga. 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 show the existence of two sticky particles models with the same velocity function 𝑒 𝑑 ( π‘₯ ) which is the entropy solution of the inviscid Burgers' equation. One of them is governed by the set of discontinuity points of 𝑒 0 . Thus, the trajectories 𝑑 ↦ 𝑋 𝑑 coincide; however one has different mass distributions πœ• π‘₯ 𝑒 𝑑 = d 𝑒 0 ∘ 𝑋 𝑑 βˆ’ 1 and πœ† ∘ 𝑋 𝑑 βˆ’ 1 . Here, πœ† denotes the Lebesgue measure.