Stability of ion-acoustic shock profiles to one-dimensional compressible Navier-Stokes-Poisson equations with large density oscillation

It is shown in [3] that the one-dimensional compressible Navier-Stokes-Poisson system admits a unique (up to a shift) small-amplitude smooth traveling wave and this traveling wave is time-asymptotically nonlinear stable under suitably small smooth zero-mass perturbations. This paper will show that similar results still hold even for certain large initial data. Our main strategy is to use the smallness of the strength of traveling wave solution to regulate the possible growth of the solutions of the perturbation equation, and then obtain the desired uniform-in-time upper and lower bounds on the specific volume.