Traveling waves solutions of isothermal chemical systems with decay
Abbreviated Journal Title
J. Differ. Equ.
Microbial growth in a flow reactor; Isothermal chemical systems with; decay; Traveling wave; Existence; Non-existence; BIO-REACTOR MODEL; CRITICAL NONLINEARITY; CUBIC AUTOCATALYSIS; SELF-SIMILARITY; STEADY-STATES; DYNAMICS; PROPAGATION; Mathematics
This article studies propagating traveling waves in a class of reaction diffusion systems which include a model of microbial growth and competition in a flow reactor proposed by Smith and Zhao , and isothermal autocatalytic systems in chemical reaction of order m with a decay order n, where m and n are positive integers and m not equal n. A typical system in autocatalysis is A + 2B -> 3B (with rate k(1) ab(2)) and B -> C (with rate k(2)b), where m = 2 and n = 1, involving two chemical species, a reactant A and an auto-catalyst B whose diffusion coefficients, D-A and D-B, are unequal due to different molecular weights and/or sizes. Here a is the concentration density of A, b that of B and C an inert chemical species. The two constants k(1) and k(2) are material constants measuring the relative strength of respective reactions. It is shown that there exist traveling waves when m > 1 and n = 1 with suitable relation between the ratio D-B/D-A, traveling speed c and rate constants k(1), k(2). On the other hand, it is proved that there exists. no traveling wave when one of the chemical species is immobile, D-B =0 or n > m for all choices of other parameters. (C) 2014 Elsevier Inc. All rights reserved.
Journal of Differential Equations
"Traveling waves solutions of isothermal chemical systems with decay" (2015). Faculty Bibliography 2010s. 6766.