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Semi-hyperbolic patches of solutions to the two-dimensional compressible magnetohydrodynamic equations

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Supported by NSF of China (11301326) and the grant of the first-class Discipline of Universities in Shanghai
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  • We construct semi-hyperbolic patches of solutions, in which one family out of two families of wave characteristics start on sonic curves and end on transonic shock waves, to the two-dimensional (2D) compressible magnetohydrodynamic (MHD) equations. This type of flow patches appear frequently in transonic flow problems. In order to use the method of characteristic decomposition to construct such a flow patch, we also derive a group of characteristic decompositions for 2D self-similar MHD equations.

    Mathematics Subject Classification: Primary: 35L65, 35J70, 35R35; Secondary: 35J65.


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  • Figure 1.  Pseudosonic curve. (Ⅰ) Keldysh type; (Ⅱ) Tricomi type

    Figure 2.  A semi-hyperbolic patch

    Figure 3.  Left: small Goursat problem; right: global solution

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