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March  2019, 18(2): 931-942. doi: 10.3934/cpaa.2019045

## Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation

 Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-2, India

* Corresponding author

Received  March 2018 Revised  May 2018 Published  October 2018

Fund Project: The first author is supported by University Grant Commission, Government of India (Sr. No. 2121540947, Ref No: 20/12/2015(ⅱ)EU-V). The second author is supported by Science and Engineering Research Board, Department of Science and Technology, Government of India (Ref No: SB/FTP/MS-047/2013).

In this article, we study the Riemann problem for a strictly hyperbolic system of conservation laws under the linear approximation of flux functions with three parameters. The approximation does not affect the structure of Riemann problem. Furthermore, we prove that the Riemann solution to the approximated system converges to the original system as the perturbation parameter tends to zero.

Citation: Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure & Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045
##### References:

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##### References:
Riemann solution of (1) and (5) in the phase plane
The Riemann solution of (4) and (5) is R+J when $u_{-}<u_+$
The Riemann solution of (4) and (5) is S+J when $u_{+}<u_{-}<u_{+}+1.$
The Riemann solution of (4) and (5) is $\delta{S}$ when $u_{-}\geq{u}_{+}+1$
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