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Stability of Delta Shock Solution for the Simplified Magnetohydrodynamics Equations Under the Linear Flux-Function Perturbation

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Abstract

The stability of delta shock solution for the simplified magnetohydrodynamics equations is investigated carefully under the linear flux-function perturbation. Five different structures of Riemann solutions for our perturbed equations are solved in completely explicit situations. By analyzing all the arisen circumstances carefully, we prove rigorously that the limits of Riemann solutions for our perturbed equations are in well agreement with those for the original ones as the perturbation parameter vanishes. In particular, the formation of delta shock wave is well observed in the ultimate limiting state.

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Funding

This work is partially supported by Natural Science Foundation of Shandong Province (ZR2019MA058).

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  1. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, P.R. China

    **aolin Liu & Chun Shen

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  1. **aolin Liu
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  2. Chun Shen
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Correspondence to Chun Shen.

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Liu, X., Shen, C. Stability of Delta Shock Solution for the Simplified Magnetohydrodynamics Equations Under the Linear Flux-Function Perturbation. Acta Appl Math 183, 1 (2023). https://doi.org/10.1007/s10440-022-00548-0

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