Some Results on the Stability of Non-classical Shock Waves

Abstract

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.