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Global Existence and Stability of Shock Front Solution to 1-D Piston Problem for Exothermically Reacting Euler Equations

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Abstract

In this paper, we are concerned with the global existence and stability of strong shock front for one-dimensional piston problem. We use the exothermically reacting Euler equations as a mathematical model to describe the gas motion. Under the assumptions that the total variations of initial data and the perturbation of piston velocity are sufficiently small, we establish the global existence and asymptotic behavior of entropy solutions including a strong shock front without restriction on the strength. A modified fractional wave front tracking scheme is developed and a modified Glimm-type functional is carefully designed.

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Acknowledgements

This work was supported in part by the NSFC Project 11801549, NSFC Project 11971024, NSFC Project 11421061, the 111 Project B08018, Natural Science Foundation of Shanghai 15ZR1403900 and the Initial Scientic Research Fund for Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences.

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Authors and Affiliations

  1. Wuhan Institute of Physics and Mathematics Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan, 430071, People’s Republic of China

    Jie Kuang

  2. Department of Mathematics School of Science, Wuhan University of Technology, Wuhan, 430070, People’s Republic of China

    Qin Zhao

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  1. Jie Kuang
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  2. Qin Zhao
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Correspondence to Qin Zhao.

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Communicated by G.-Q. Chen

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Kuang, J., Zhao, Q. Global Existence and Stability of Shock Front Solution to 1-D Piston Problem for Exothermically Reacting Euler Equations. J. Math. Fluid Mech. 22, 22 (2020). https://doi.org/10.1007/s00021-020-0486-6

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