The Stability of Vector Renewal Equations Pertaining to Heterogeneous Chemical Reaction

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.