TY - JOUR
T1 - Some Results on the Stability of Non-classical Shock Waves
JO - Journal of Partial Differential Equations
VL - 1
SP - 25
EP - 38
PY - 1998
DA - 1998/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5552.html
KW - Conservation laws
KW - shock waves
KW - stability
KW - overcompressive
KW - undercompressive
AB -  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.