  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.
