Stability Analysis for a Class of Heterogeneous Catalysis Models

TL;DR

This paper proves exponential stability for a class of heterogeneous catalysis models in a 3D pore setting, analyzing conditions for stability and potential instability in the system.

Contribution

It introduces a stability analysis framework for heterogeneous catalysis models in cylindrical geometries, establishing conditions for exponential stability.

Findings

Equilibria are normally stable under certain parameter conditions.

Solutions are attracted exponentially to equilibrium.

Potential instability scenarios are discussed.

Abstract

We prove stability for a class of heterogeneous catalysis models in the $L_p$-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a reasonable condition on the involved parameters, we show that given equilibria are normally stable, i.e. solutions are attracted at an exponential rate. The potential incidence of instability is discussed as well.