Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 37, Issue 8, Pages 4439-4460Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2017190
Keywords
Generalized Chaplygin model; shadow waves; entropy solutions; delta shocks; Bessel functions
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Funding
- Serbian Ministry of Science [01174024, 11144006]
- APV Secretariat for Science [114-451-2098]
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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.
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