# American Institute of Mathematical Sciences

August  2017, 37(8): 4439-4460. doi: 10.3934/dcds.2017190

## On the uniqueness of solution to generalized Chaplygin gas

 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia

* Corresponding author: Marko Nedeljkov

Received  June 2016 Revised  May 2017 Published  April 2017

Fund Project: The first author is partially supported by the projects OI174024 and III44006, Serbian Ministry of Science and by the Project 114-451-2098, APV Secretariat for Science

The main object of the paper is finding a unique solution to Riemann problem for generalized Chaplygin gas model. That is a model of the dark energy in Universe introduced in the last decade. It permits an infinite mass concentration so one has to consider solutions containing the Dirac delta function. Although it was easy to construct solution to any Riemann problem, the usual admissibility conditions, overcompressiveness, do not exclude unwanted delta-type waves when a classical solution exists. We are using Shadow Wave approach in order to solve that uniqueness problem since they are well adopted for using Lax entropy–entropy flux conditions and there is a rich family of convex entropies.

Citation: Marko Nedeljkov, Sanja Ružičić. On the uniqueness of solution to generalized Chaplygin gas. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4439-4460. doi: 10.3934/dcds.2017190
##### References:

show all references

##### References:
Classical waves
Overcompressive SDW vs. S1+S2
Energy entropy condition
Inequalities (15) and (16)
Inequalities (15) and (16) are not enough to prove non-positivity of $\hat{E}_{\lambda}^1$
Entropies at $\Gamma_{ss}$ curve – the first entropy pair
Entropies at $\Gamma_{ss}$ curve – the second entropy pair
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