# Stability of the Riemann solution for a 2 × 2 strictly hyperbolic system of conservation laws

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## Abstract

In this work, we study the system of conservation laws that is strictly hyperbolic and whose Riemann solution contains delta shock waves as well as classical elementary waves. In order to study stability, we consider the linear approximation of flux functions with three parameters. The approximation does not affect the structure of Riemann solution. Furthermore, we prove that the solution of the Riemann problem for the approximated system converges to the solution of the original system when the perturbation parameter tends to zero.

## Keywords

Riemann problem delta shock wave strictly hyperbolic system flux approximation## Notes

### Acknowledgements

We thank the referees for their valuable comments and suggestions. The first author (Anupam Sen) is supported by University Grant Commission, Government of India (Sr. No. 2121540947, Ref. No. 20/12/2015(ii)EU-V). The third author (Dia Zeidan) has been supported by the Scientific Research Support Fund, Ministry of Higher Education & Scientific Research through the German Jordanian University (Fund No. Bas/1/05/2016), Amman, Jordan.

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