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Some results on the stability of non-classical shock waves. (English) Zbl 0903.35006
Summary: Part 1 of this paper establishes the infinite-time stability of a class of over-compressive viscous shock waves; the equations studied here are a mathematical analogue of those of magnetohydrodynamics. Part 2 communicates a rather general short-time stability result for undercompressive shock waves in several space dimensions; technically, this is an easy extension of Majda’s corresponding result for Laxian shock waves.

MSC:
35B35 Stability in context of PDEs
35L65 Hyperbolic conservation laws
76W05 Magnetohydrodynamics and electrohydrodynamics
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