Blow up at the hyperbolic boundary for a 2x2 system arising from chemical engineering

TL;DR

This paper investigates a hyperbolic boundary blow-up phenomenon in a 2x2 conservation law system modeling heatless gas adsorption, revealing conditions under which the solution velocity becomes unbounded at the boundary.

Contribution

It constructs solutions exhibiting blow-up at the hyperbolic boundary for a chemically motivated 2x2 system with variable velocity.

Findings

Velocity blows up at the hyperbolic boundary t=0

Solution behavior is characterized near the boundary

The model extends understanding of boundary singularities in conservation laws

Abstract

We consider an initial boundary value problem for a 2x2 system of conservation laws modeling heatless adsorption of a gaseous mixture with two species and instantaneous exchange kinetics, close to the system of Chromatography. In this model the velocity is not constant because the sorption effect is taken into account. Exchanging the roles of the x, t variables we obtain a strictly hyperbolic system with a zero eigenvalue. Our aim is to construct a solution with a velocity which blows up at the corresponding characteristic "hyperbolic boundary" {t = 0}.