The development of travelling waves in cubic auto-catalysis with different rates of diffusion
Abbreviated Journal Title
cubic auto-catalysis; travelling wave; minimum speed; reaction-diffusion; ISOTHERMAL CHEMICAL-SYSTEM; PROPAGATING FRONTS; STABILITY; EXISTENCE; EQUATIONS; DECAY; ACID; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical
In this paper we study the isothermal auto-catalytic chemical reaction, A + 2B -> 3 B involving two chemical species A and B. Their diffusion coefficients, denoted by D-A and D-B, respectively, are unequal, which happens when the two chemical species have different molecular weights. The propagating reaction-diffusion waves that may develop from a local initial input of the auto-catalyst, B, are investigated in one spatial dimension. We show the existence of travelling wave solutions for all propagation speed v >= v(2)*, with v(2)* a function of the ratio of the diffusion 2 2 rates of the species A and B, representing the estimated minimum propagation speed. Our result improves significantly on the results of early works. In addition, we show the non-existence of travelling wave solutions when v <= v(2), where v(2) depends on the ratio of the diffusion rates of the species A and B. We believe that our non-existence result is the first of the kind for equations of the isothermal auto-catalytic chemical reaction type. We also demonstrate similar results on the general isothermal auto-catalytic chemical reaction, A + nB -> (n + 1) B, of n-th order with it > 1. (c) 2006 Elsevier B.V. All rights reserved.
Physica D-Nonlinear Phenomena
"The development of travelling waves in cubic auto-catalysis with different rates of diffusion" (2007). Faculty Bibliography 2000s. 7543.