Article Contents
Article Contents

# The asymptotic limits of solutions to the Riemann problem for the scaled Leroux system

• * Corresponding author: Chun Shen.
Chun Shen is supported by NSFC (11441002) and Shandong Provincial Natural Science Foundation (ZR2014AM024), Wancheng Sheng is supported by NSFC (11371240) and Meina Sun is supported by NSFC (11271176).
• The Riemann problem for the scaled Leroux system is considered. It is proven rigorously that the Riemann solutions for the scaled Leroux system converge to the corresponding ones for a non-strictly hyperbolic system of conservation laws when the perturbation parameter tends to zero. In addition, some interesting phenomena are displayed in the limiting process, such as the formation of delta shock wave and a rarefaction (or shock) wave degenerates to be a contact discontinuity.

Mathematics Subject Classification: Primary:35L65, 35L67;Secondary:35B25.

 Citation:

• Figure 1.  The phase plane for the scaled Leroux system (1.2) when $u_{-}<0$, left for $\varepsilon>0$ and right for the limit $\varepsilon\rightarrow0$ situation.

Figure 2.  The phase plane for the scaled Leroux system (1.2) when $u_{-}>0$, left for $\varepsilon>0$ and right for the limit $\varepsilon\rightarrow0$ situation.

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