ON A TRANSIENT NONLINEAR ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH A POINT-SOURCE INITIAL CONDITION

We revisit the analysis of a transient nonlinear reaction-diffusion equation describing two-particle coalescence or, alternatively, annihilation in an infinite domain. On nondimensionalizing the governing equations, we find that the problem is, in general, free of dimensionless parameters, indicating that the original work, which was purported to be for the slow reaction limit, is instead better interpreted as being for small times. By means of analysis using similarity-like variables, we also find that the delta-peaked initial condition used in the original analysis leads to an unexpected and easily overlooked restriction on the reaction order, which cannot be greater than 3; the same applies for two-term regular perturbation expansions that are valid for short times, and which we also determine. The full equations are then solved numerically for all times and the solutions are found to agree well with the analytical results that are available for short times.