THE STRUCTURE AND PROPERTIES OF AN APPROXIMATE SOLUTION TO A SYSTEM OF REACTION-DIFFUSION EQUATIONS.

Abstract

Several formal asymptotic expansions for a pair of coupled reaction-diffusion equations, constructed by Kapila and Aris for small time and large time, assuming discontinuous initial data, are rigorously justified. The system studied models the diffusion and reaction of chemical species, where the reaction is of the form A + B → C. The solution of the system can be represented as a power series expansion in time, which is shown to converge for time → ∞. A number of other mathematical questions associated with the asymptotic expansions, such as existence, uniqueness, and boundedness of solutions to various nonlinear equations, are studied.