Stability of shock solutions to piston problem for the magnetohydrodynamics


This article is devoted to studying one-dimensional piston problem for the compressible Magnetohydrodynamics when the piston is pushed forward relatively. If the initial data and the piston speed are both given some small \(\mathrm {BV}\) perturbations, then global stability of large shock waves to this problem has been established, and the long time behavior has been also considered.

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The research of Min Ding was supported in part by the National Natural Science Foundation of China under Grant Nos. 11701435 and 11626176, and in part by “the Fundamental Research Funds for the Central Universities(WUT: 2018IVB013 and 2018IB015)”.

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Ding, M. Stability of shock solutions to piston problem for the magnetohydrodynamics. Z. Angew. Math. Phys. 72, 59 (2021).

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  • Shock waves
  • Magnetohydrodynamics
  • Wave interaction
  • Long time behavior

Mathematics Subject Classification

  • 35B35
  • 35L67
  • 76L05
  • 76W05
  • 35B40