Applied Mathematics and Mechanics

, Volume 22, Issue 9, pp 1064–1073 | Cite as

The formation of shock waves of the equations of magnetohydrodynamics

  • Dong Li-ming
  • Shi Yi-peng


The property of fluid field of one-dimensional magnetohydrodynamics (MHD) transverse flow after the appearance of singularity is discussed. By the method of iteration, the strong discontinuity (shock wave) and entropy solution are constructed and the estimations on the singularity of the solution near the point of blow up are obtained.

Key words

MHD transverse flow shock wave entropy solutions 

CLC number



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  1. [1]
    Sideris T C. Formation of singularities in three dimensional compressible fluid [J].Comm Math Phys, 1985,101(3):475–485.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Rammaha M A. On the formation of singularities in magneto-hynanic waves[J].J Math Anal Appl, 1994,188(3):940–955.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    KONG De-xing. Cauchy problem for quasilinear hyperbolic systems[D]. Thesis for PhD Degree. Shanghai: Fudan University, 1993. (in Chinese)Google Scholar
  4. [4]
    DONG Li-ming. Formation of shock waves by quasilinear hyperbolic equations[D]. Thesis for PhD Degree. Shanghai: Fudan University, 1999. (in Chinese)Google Scholar
  5. [5]
    Lebaud M P. Description de ca formation d'un choc dans le p-systems [J].J Math Pure Appl, 1994,73(6):523–565.zbMATHMathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics All rights reserved 1980

Authors and Affiliations

  • Dong Li-ming
    • 1
  • Shi Yi-peng
    • 2
  1. 1.Department of Applied MathematicsEast-China University of Science and TechnologyShanghaiP R China
  2. 2.Institute of MathematicsFudan UniversityShanghaiP R China

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