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June  2014, 7(2): 205-218. doi: 10.3934/krm.2014.7.205

Non-existence and non-uniqueness for multidimensional sticky particle systems

Alberto Bressan 1, and  Truyen Nguyen 2,

1. 

Department of Mathematics, Penn State University, University Park, Pa.16802
2. 

Department of Mathematics, University of Akron, Akron, OH 44325, United States

Received  December 2013 Revised  February 2014 Published  March 2014

The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or (ii) no sticky solution, not even locally in time. In both cases the initial density is smooth with compact support, while the initial velocity field is continuous.
Keywords: non-uniqueness, Sticky particle systems, non-existence, conservation laws., pressureless Euler system.
Mathematics Subject Classification: Primary: 35L03, 35L65, 35L80; Secondary: 70F1.
Citation: Alberto Bressan, Truyen Nguyen. Non-existence and non-uniqueness for multidimensional sticky particle systems. Kinetic & Related Models, 2014, 7 (2) : 205-218. doi: 10.3934/krm.2014.7.205
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show all references

References:
[1]

Comm. Part. Diff. Eq., 24 (1999), 2173-2189. doi: 10.1080/03605309908821498.  Google Scholar

[2]

J. Math. Pures Appl., 99 (2013), 577-617. doi: 10.1016/j.matpur.2012.09.013.  Google Scholar

[3]

SIAM J. Numer. Anal., 35 (1998), 2317-2328. doi: 10.1137/S0036142997317353.  Google Scholar

[4]

Comm. Math. Phys., 177 (1996), 349-380. doi: 10.1007/BF02101897.  Google Scholar

[5]

Comm. Math. Phys., 222 (2001), 117-146. doi: 10.1007/s002200100506.  Google Scholar

[6]

SIAM J. Math. Anal., 41 (2009), 1340-1365. doi: 10.1137/090750809.  Google Scholar

[7]

SIAM J. Math. Anal., 40 (2008), 754-775. doi: 10.1137/070704459.  Google Scholar

[8]

preprint, (2013). Google Scholar

[9]

Diff. Integral Equat., 14 (2001), 1077-1092.  Google Scholar

[10]

Astro. & Astrophys., 5 (1970), 84-89. Google Scholar

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