Ion-acoustic shock in a collisional plasma

TL;DR

This paper investigates ion-acoustic shock waves in collisional plasmas, establishing existence, approximation, and stability of shock profiles under specific dissipative conditions.

Contribution

It introduces a rigorous analysis of ion-acoustic shocks, including existence, approximation by KdV-Burgers profiles, and stability in collisional plasma environments.

Findings

Existence and uniqueness of small-amplitude shock waves.

Approximation of shock profiles by KdV-Burgers equations.

Large-time stability of traveling wave solutions.

Abstract

The paper is concerned with the propagation of ion-acoustic shock waves in a collision dominated plasma. We firstly establish the existence and uniqueness of a small-amplitude smooth travelling wave, then justify its approximation to the shock profile of the KdV-Burgers equations in a suitable asymptotic regime where dissipation in terms of viscosity coefficient is much stronger than dispersion by the Debye length, and prove in the end the large time asymptotic stability of travelling waves under suitably small smooth perturbations.