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Linear degeneracy and shock waves. (English) Zbl 0756.35048
Jump discontinuities in weak solutions of hyperbolic systems of conservation laws, are investigated, which are associated with linearly degenerate modes. It is assumed that the integral manifolds of the corresponding eigenspace bundle are compact. Multiple eigenvalues of the fields are permitted.
First, the geometry of such linear degenerate fields are established. Then it is shown that there exists also shocks for these modes, which are not of the familiar contact discontinuity type, and that these shocks have sometimes viscous profiles. As an application, this is demonstrated (independent of the dissipation) for certain shocks associated to the rotational Alfvén modes of the system of magnetohydrodynamic equations.

35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics
Full Text: DOI EuDML
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