Electron. J. Differential Equations,
Vol. 2016 (2016), No. 320, pp. 125.
Structural stability of Riemann solutions for strictly
hyperbolic systems with three piecewise constant states
Xuefeng Wei, Chun Shen
Abstract:
This article concerns the wave interaction problem for a
strictly hyperbolic system of conservation laws whose Riemann
solutions involve delta shock waves. To cover all situations,
the global solutions are constructed when the initial data are taken
as three piecewise constant states. It is shown that the Riemann
solutions are stable with respect to a specific small perturbation of
the Riemann initial data.
In addition, some interesting nonlinear phenomena are captured during
the process of constructing the solutions, such as the generation and
decomposition of delta shock waves.
Submitted September 22, 2016. Published December 14, 2016.
Math Subject Classifications: 35L65, 35L67, 76N15.
Key Words: Delta shock wave; wave interaction; Riemann problem;
strict hyperbolicity.
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Xuefeng Wei
School of Mathematics and Statistics Science
Ludong University
Yantai, Shandong Province 264025, China
email: 50816179@qq.com


Chun Shen
School of Mathematics and Statistics Science
Ludong University
Yantai, Shandong Province 264025, China
email: shenchun3641@sina.com

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