The stability of vector renewal equations pertaining to heterogeneous chemical reaction systems

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Abstract
For a class of vector renewal equations arising in the theory of spatially nonuniform chemical reaction processes, stability conditions are given in terms of the physicochemical operators D and K. In particular, we provide conditions for the stability of an initially uniform, multicomponent film bounding a planar catalytic surface, and for the asymptotic stability of a reaction system composed of a population of catalyst particles. We obtain such results by identifying a sup norm which is naturally induced from the factors that symmetrize D and/or K. Further, we exhibit conditions under which a special class of vector renewal equations has positive solutions.

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