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

Authors:
A. E. DeGance and L. E. Johns

Journal:
Quart. Appl. Math. **34** (1976), 69-83

MSC:
Primary 82.45

DOI:
https://doi.org/10.1090/qam/449376

MathSciNet review:
449376

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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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Additional Information

DOI:
https://doi.org/10.1090/qam/449376

Article copyright:
© Copyright 1976
American Mathematical Society