Global Strong Solutions for a Class of Heterogeneous Catalysis Models

TL;DR

This paper establishes conditions for the existence of unique global strong solutions to a complex mathematical model of heterogeneous catalysis involving coupled diffusion, reaction, and sorption processes in a three-dimensional pore.

Contribution

It extends classical reaction-diffusion results to heterogeneous catalysis models with coupled bulk-surface interactions and complex reaction networks.

Findings

Proved existence of unique global strong solutions under certain conditions.

Extended reaction-diffusion theory to heterogeneous catalysis scenarios.

Provided mathematical framework for analyzing catalytic processes in porous media.

Abstract

We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a diffusion-advection system inside the bulk phase and a reaction-diffusion-sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface. We assume Fickian diffusion with constant coefficients, sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure. Our main result gives sufficient conditions for the existence of a unique global strong $L^2$-solution to this model, thereby extending by now classical results on reaction-diffusion systems to the more complicated case of heterogeneous catalysis.