Viscous singular shock profiles for a system of conservation laws modeling two-phase flow

TL;DR

This paper investigates viscous singular shock profiles in a two-phase flow model, proving their existence using geometric singular perturbation theory and analyzing their convergence and growth behaviors.

Contribution

It introduces a novel application of geometric singular perturbation theory to establish the existence of viscous singular shocks in two-phase flow models.

Findings

Existence of viscous singular shock profiles proven.

Weak convergence and growth rates of solutions characterized.

Unbounded solution families analyzed for stability and behavior.

Abstract

This paper is concerned with singular shocks for a system of conservation laws modeling incompressible two-phase fluid flow. We prove the existence of viscous profiles using the Geometric Singular Perturbation Theory. Weak convergence and growth rates of the unbounded family of solutions are also obtained.