Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry

We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e. exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface chemistry for a prototypical chemical reactor. For the resulting reaction–diffusion systems with linear boundary conditions on the normal mass fluxes, but at the same time nonlinear boundary conditions on the concentrations itself, we provide analytic properties such as local-in-time well-posedness, positivity, a priori bounds and comment on steps towards global existence of strong solutions in the class $$\mathrm {W}^{(1,2)}_p(J \times \Omega ; {{\,\mathrm{{\mathbb {R}}}\,}}^N)$$ W p ( 1 , 2 ) ( J × Ω ; R N ) , and of classical solutions in the Hölder class $$\mathrm {C}^{(1+\alpha , 2 + 2\alpha )}({\overline{J}} \times {\overline{\Omega }}; {{\,\mathrm{{\mathbb {R}}}\,}}^N)$$ C ( 1 + α , 2 + 2 α ) ( J ¯ × Ω ¯ ; R N ) . Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle.