Singular Shocks in a Chromatography Model

TL;DR

This paper analyzes a nonlinear chromatography model, explaining the emergence of singular shocks using geometric singular perturbation theory, and proves the existence of viscous solutions in a regularized system.

Contribution

It provides a rigorous explanation and proof of singular shocks in chromatography models using geometric singular perturbation theory.

Findings

Existence of viscous solutions to the regularized model.

Coherent explanation of unbounded solutions (singular shocks).

Application of geometric singular perturbation theory to chromatography.

Abstract

We consider a system of two equations that can be used to describe nonlinear chromatography and produce a coherent explanation and description of the unbounded solutions (singular shocks) that appear in M. Mazzotti's model. We use the methods of Geometric Singular Perturbation Theory, to show existence of a viscous solution to Dafermos-DiPerna regularization.