Riemann problem for the relativistic generalized Chaplygin Euler equations

Meixiang  Huang; Zhi-Qiang Shao

doi:10.3934/cpaa.2016.15.127

Article Contents

2016, Volume 15, Issue 1: 127-138. Doi: 10.3934/cpaa.2016.15.127

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Riemann problem for the relativistic generalized Chaplygin Euler equations

Meixiang Huang^1, and
Zhi-Qiang Shao^2,

1.
College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108
2.
Department of Mathematics, Fuzhou University, Fuzhou 350002

Received: March 31, 2015

Revised: August 31, 2015

Published: December 2015

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Abstract

The Riemann problem for the relativistic generalized Chaplygin Euler equations is considered. Its two characteristic fields are genuinely nonlinear, but the nonclassical solutions appear. The formation of mechanism for $\delta-$shock is analyzed, that is the one-shock curve and the two-shock curve do not intersect each other in the phase plane. The Riemann solutions are constructed, and the generalized Rankine-Hugoniot conditions and the $\delta-$entropy condition are clarified. Moreover, under the generalized Rankine-Hugoniot conditions and entropy condition, we constructively obtain $\delta-$shock waves.

Keywords:

Relativistic Euler equations,
Riemann problem,
delta shock wave,
generalized Rankine-Hugoniot conditions,
generalized Chaplygin.

Mathematics Subject Classification: 35L65, 35L67.

Citation:

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References

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