@article {He:1993:0022-2526:195,
title = "Shock Wave Tracking for Hyperbolic Systems Exhibiting Local Linear Degeneracy",
journal = "Studies in Applied Mathematics",
parent_itemid = "infobike://bpl/sapm",
publishercode ="bp",
year = "1993",
volume = "89",
number = "3",
publication date ="1993-08-01T00:00:00",
pages = "195-232",
itemtype = "ARTICLE",
issn = "0022-2526",
eissn = "1467-9590",
url = "https://www.ingentaconnect.com/content/bpl/sapm/1993/00000089/00000003/art00002",
doi = "doi:10.1002/sapm1993893195",
author = "He, Yuanping and Moodie, T. Bryant",
abstract = "Extending the results of our previous study [2], we now investigate the propagation of interior shocks corresponding to the signaling problem of smallamplitude, highfrequency type. We derive a formula for the shock front and show that the previously constructed asymptotic
solution is valid on both sides of this front. This solution is further distinguished to a higher order in which the effects of material inhomogeneity are accounted for. Moreover, if = (u, x) represents the eigenvalue under consideration, we show that the singlewavemode
boundary disturbance of [2] can lead only to a shock. We also derive an entropy condition for the shock wave. As an application of our theory, the fluidfilled hyperelastic tube problem of [7] is further examined and an example calculation made in which we show that
a compressive shock wave is generated at the shockinitiation point. This demonstration is effected as a particular example of the solution to a general bifurcation problem.",
}