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Kinetic and Related Models (KRM)
 

Non-existence and non-uniqueness for multidimensional sticky particle systems
Pages: 205 - 218, Issue 2, June 2014

doi:10.3934/krm.2014.7.205      Abstract        References        Full text (419.1K)           Related Articles

Alberto Bressan - Department of Mathematics, Penn State University, University Park, Pa.16802, United States (email)
Truyen Nguyen - Department of Mathematics, University of Akron, Akron, OH 44325, United States (email)

1 F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness, Comm. Part. Diff. Eq., 24 (1999), 2173-2189.       
2 Y. Brenier, W. Gangbo, G. Savaré and M. Westdickenberg, Sticky particle dynamics with interactions, J. Math. Pures Appl., 99 (2013), 577-617.       
3 Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws, SIAM J. Numer. Anal., 35 (1998), 2317-2328.       
4 W. E, Yu. Rykov and Y. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Comm. Math. Phys., 177 (1996), 349-380.       
5 F. Huang and Z. Wang, Well posedness for pressureless flow, Comm. Math. Phys., 222 (2001), 117-146.       
6 L. Natile and G. Savaré, A Wasserstein approach to the one-dimensional sticky particle system, SIAM J. Math. Anal., 41 (2009), 1340-1365.       
7 T. Nguyen and A. Tudorascu, Pressureless Euler/Euler-Poisson systems via adhesion dynamics and scalar conservation laws, SIAM J. Math. Anal., 40 (2008), 754-775.       
8 T. Nguyen and A. Tudorascu, One-dimensional pressureless gas systems with/without viscosity, preprint, (2013).
9 M. Sever, An existence theorem in the large for zero-pressure gas dynamics, Diff. Integral Equat., 14 (2001), 1077-1092.       
10 Y. B. Zeldovich, Gravitational instability: An approximate theory for large density perturbations, Astro. & Astrophys., 5 (1970), 84-89.

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