`ISRN Mathematical PhysicsVolume 2012 (2012), Article ID 506863, 12 pageshttp://dx.doi.org/10.5402/2012/506863`
Research Article

## Systems of Sticky Particles Governed by Burgers' Equation

Département de Mathématiques et Informatique, Faculté des Sciences, Université 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.

1. J. M. Burgers, The Non-Linear Diffusion Equation, D. Reidel, Dordrecht, The Netherlands, 1974.
2. S. N. Gurbatov, A. N. Malakov, and A. I. Saichev, Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles, Manchester University Press, 1991.
3. E. Hopf, “The partial differential equation ${u}_{t}+u{u}_{x}=\mu {u}_{xx}$,” Communications on Pure and Applied Mathematics, vol. 3, pp. 201–230, 1950.
4. Y. Brenier and E. Grenier, “Sticky particles and scalar conservation laws,” SIAM Journal on Numerical Analysis, vol. 35, no. 6, pp. 2317–2328, 1998.
5. W. E. Yu, G. Rykov, and Y. G. Sinai, “Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics,” Communications in Mathematical Physics, vol. 177, no. 2, pp. 349–380, 1996.
6. S. F. Shandarin and Y. B. Zeldovich, “The large-scale structure of the universe: turbulence, intermittency, structures in a self-gravitating medium,” Reviews of Modern Physics, vol. 61, no. 2, pp. 185–220, 1989.
7. A. Dermoune and O. Moutsinga, “Generalized variational principles,” in Séminaire de Probabilités, XXXVI, vol. 1801 of Lecture Notes in Mathematics, pp. 183–193, Springer, Berlin, Germany, 2003.
8. O. Moutsinga, “Convex hulls, sticky particle dynamics and pressure-less gas system,” Annales Mathématiques Blaise Pascal, vol. 15, no. 1, pp. 57–80, 2008.
9. O. Moutsinga, “Burgers' equation and the Sticky particles model,” submitted to Journal of Mathematical Physics.
10. A. F. Fillipov, “Differential equations with discontinuous right hand side,” AMS Translation Journals, vol. 42, no. 2, pp. 199–231, 1964.