Small, medium and large shock waves for non-equilibrium radiation hydrodynamic

TL;DR

This paper investigates shock wave profiles in a radiation hydrodynamics model, establishing conditions for their existence, continuity, and the presence of temperature spikes, with rigorous thresholds for different shock types.

Contribution

It provides a rigorous analysis of shock profiles in a hyperbolic-elliptic radiation hydrodynamics system, including existence, continuity, and temperature spike criteria.

Findings

Existence of heteroclinic connections between singular points.

Profiles can be continuous or have a single discontinuity.

A sharp threshold for the presence of a temperature maximum (Zel'dovich spike).

Abstract

We examine the existence of shock profiles for a hyperbolic-elliptic system arising in radiation hydrodynamics. The algebraic-differential system for the wave profile is reduced to a standard two-dimensional form that is analyzed in details showing the existence of heteroclinic connection between the two singular points of the system for any distance between the corresponding asymptotic states of the original model. Depending on the location of these asymptotic states, the profile can be either continuous or possesses at most one point of discontinuity. Moreover, a sharp threshold relative to presence of an internal absolute maximum in the temperature profile --also called {\sf Zel'dovich spike}-- is rigourously derived.