INTERACTIONS OF DELTA SHOCK WAVES FOR A CLASS OF NONSTRICTLY HYPERBOLIC SYSTEM OF CONSERVATION LAWS

Yanyan Zhang; Yu Zhang

doi:10.11948/20190228

2020 Volume 10 Issue 6

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Yanyan Zhang, Yu Zhang. INTERACTIONS OF DELTA SHOCK WAVES FOR A CLASS OF NONSTRICTLY HYPERBOLIC SYSTEM OF CONSERVATION LAWS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2381-2399. doi: 10.11948/20190228

Citation:

Yanyan Zhang, Yu Zhang. INTERACTIONS OF DELTA SHOCK WAVES FOR A CLASS OF NONSTRICTLY HYPERBOLIC SYSTEM OF CONSERVATION LAWS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2381-2399. doi: 10.11948/20190228

INTERACTIONS OF DELTA SHOCK WAVES FOR A CLASS OF NONSTRICTLY HYPERBOLIC SYSTEM OF CONSERVATION LAWS

Yanyan Zhang¹,
Yu Zhang^2, ,

1.
College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
2.
Department of Mathematics, Yunnan Normal University, Kunming 650500, China

Corresponding author: Email address:zyy@xynu.edu.cn(Y. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (11501488, 11801490), the Scientific Research Foundation of Xinyang Normal University(No. 0201318), Nan Hu Young Scholar Supporting Program of XYNU, Yunnan Applied Basic Research Projects (2018FD015) and the Scientific Research Foundation Project of Yunnan Education Department (2018JS150)

Abstract

Abstract

In this paper, we study the perturbed Riemann problem for a class of nonstrictly hyperbolic system of conservation laws, and focuse on the interactions of delta shock waves with the shock waves and the rarefaction waves. The global solutions are constructed completely with the method of splitting delta function. In solutions, we find a new kind of nonclassical wave, which is called delta contact discontinuity with Dirac delta function in both components. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. Moreover, by letting perturbed parameter " tend to zero, we analyze the stability of Riemann solutions.
- Nonstrictly hyperbolic system /
- wave interaction /
- delta shock waves /
- delta contact discontinuity /
- split delta function
MSC: 35L65, 35L67

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References

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