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- Differential equations; Ecological systems; Comparison theorems; Banach spaces
Let T be the temperature and n the concentration of a combustible substance. A simple model governing the combustion of the material is given by [see pdf for notations] (1.1) where the constant Q is the heat of reaction; the constants Kl , K2 are thermal, material diffusion coefficients; the term exp(-E/RT) is the Arrenhius rate factor; E is the activation energy; and R is the univeral gas constant. Equations (1.1) are considered on a bounded domain ^ with the boundary conditions [see pdf for notations] (1.2) together with initial conditions [see pdf for notations] (1.3) under the assumption T0(x) ^ To . Here ^ denotes an outward normal. A discussion of the derivation of the general equations of chemical kinetics may be found in the books by Gavalas  and Frank-Kamenetzky . The particular model (1.1) to (1.3) is discussed by Gelfand  and Sattinger . See also Hlavacek and Hofmann 128].