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The fast-sorption and fast-surface-reaction limit of a heterogeneous catalysis model. (English) Zbl 1459.35243

Summary: Within this paper, we consider a heterogeneous catalysis system consisting of a bulk phase \(\Omega\) (chemical reactor) and an active surface \(\Sigma=\partial\Omega\) (catalytic surface), between which chemical substances are exchanged via adsorption (transport of mass from the bulk boundary layer adjacent to the surface, leading to surface-accumulation by a transformation into an adsorbed form) and desorption (the reverse process). Quite typically, as is the purpose of catalysis, chemical reactions on the surface occur several orders of magnitude faster than, say, chemical reactions within the bulk phase, and sorption processes are often quite fast as well. Starting from the non-dimensional version, different limit models, especially for fast surface chemistry and fast sorption at the surface, are considered. For a particular model problem, questions of local-in-time existence of strong and classical solutions and positivity of solutions are addressed.

MSC:

35K57 Reaction-diffusion equations
35K51 Initial-boundary value problems for second-order parabolic systems
35K59 Quasilinear parabolic equations
80A30 Chemical kinetics in thermodynamics and heat transfer
92E20 Classical flows, reactions, etc. in chemistry
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