  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.
