@Article{AAMM-7-3,
author = {C., Berthon and Boutin, B. and Turpault, R.},
title = {Shock Profiles for the Shallow-Water Exner Models},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2015},
volume = {7},
number = {3},
pages = {267--294},
abstract = {<p style="text-align: justify;">This article is devoted to analyzing some ambiguities coming from a class of
sediment transport models. The models under consideration are governed by the coupling
between the shallow-water and the Exner equations. Since the PDE system turns
out to be an hyperbolic system in non conservative form, ambiguities may occur as
soon as the solution contains shock waves. To enforce a unique definition of the discontinuous
solutions, we adopt the path-theory introduced by Dal Maso, LeFLoch and
Murat [18]. According to the path choices, we exhibit several shock definitions and we
prove that a shock with a constant propagation speed and a given left state may connect
an arbitrary right state. As a consequence, additional assumptions (coming from
physical considerations or other arguments) must be chosen to enforce a unique definition.
Moreover, we show that numerical ambiguities may still exist even when a
path is chosen to select the system&#39;s solution.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2013.m331},
url = {https://global-sci.com/article/73395/shock-profiles-for-the-shallow-water-exner-models}
}