Wave propagation over shock profiles

As a wave propagates over a shock profile, there are new waves
reflecting, transmitting and moving along the profile. The rich wave
phenomenon results from the strong nonlinear nature of the shock waves,
as well as the coupling of waves for a general system of conservation
laws. For one spatial dimension, there are sub-scale waves as a result
of nonlinear coupling of distinct characteristic families. For more than
one spatial dimension, the propagation of dispersion waves over a shock
profile give rise to new wave phenomena, which we illustrate with a
simple model inspired by gas dynamics. Strongly quantitative methods
based on explicit construction of Green's function are introduced for
our analysis.