Exact solutions for a diffusion-reaction process in one dimension

This paper presents a new method for the solution of diffusion-reaction problems in one dimension. The method is used to derive some new exact results for the polymerization (cl-cl aggregation) and annihilation processes on openR and openZ. Through well-known dualities, these results have implications for the T=0 limit of the kinetic Ising model and for two interacting particle processes, the invasion and voter models. Prospectively, the method may be useful in providing one-dimensional verification for speculations in the theory of diffusion reaction.