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Every mathematical model describing physical phenomena is an approximation tomodel reality, hence has its limitations. Depending on characteristic values ofthe variables in the model, different aspects of the model and, e.g.,thermodynamic mechanisms have to be emphasised, or may be neglected in areduced limit model. Within this paper, a heterogeneous catalysis system willbe considered consisting of a bulk phase $\Omega$ (chemical reactor) and anactive surface $\Sigma = \partial \Omega$ (catalytic surface), between whichchemical substances are exchanged via adsorption (transport of mass from thebulk boundary layer adjacent to the surface, leading to surface-accumulation bya transformation into an adsorbed form) and desorption (vice versa). Quitetypically, as is the purpose of catalysis, chemical reactions on the surfaceoccur several orders of magnitude faster than, say, chemical reactions withinthe bulk, and sorption processes are often quite fast as well. Starting fromthe non-dimensional version, different limit models, especially for fastsurface chemistry and fast sorption at the surface, are considered. For aparticular model problem, questions of local-in-time existence of strong andclassical solutions, positivity of solutions and blow-up criteria for globalexistence are addressed.

The fast-sorption--fast-surface-reaction limit of a heterogeneous catalysis model