Existence and qualitative properties of kinetic functions generated by diffusive-dispersive regularizations

TL;DR

This paper studies traveling wave solutions in hyperbolic conservation laws with added diffusion and dispersion, focusing on the existence and properties of kinetic functions that determine admissible shock waves.

Contribution

It provides a comprehensive review of the existence and qualitative characteristics of kinetic functions generated by diffusive-dispersive regularizations.

Findings

Kinetic functions characterize admissible shock waves.

Existence of traveling wave solutions is established.

Qualitative properties of kinetic functions are analyzed.

Abstract

We investigate the properties of traveling wave solutions to hyperbolic conservation laws augmented with diffusion and dispersion, and review the existence and qualitative properties of the associated kinetic functions, which characterize the class of admissible shock waves selected by such regularizations.