Reaction kinetics of A plus B → 0

A method to find the exact reaction rate density function of an A + B -> 0 reaction on a finite 1D bar is derived. We consider the case where the A and B species diffuse at the same rate, have equal initial numbers, with the initial location of either species on the bar being arbitrary. The extension of the method to study A + B -> 0 on fractals is also shown. Additionally, we introduce the notion of a continual (in time) reaction front and a ceasing (in time) reaction front and provide a physical criterion for when either occurs.