Abstract
A mixing time density of [Formula: see text] on a finite one-dimensional domain is defined for general initial and boundary conditions in which [Formula: see text] and [Formula: see text] diffuse at the same rate. The density is a measure of the number of [Formula: see text] and [Formula: see text] particles that mix through the center of the reaction zone. It also corresponds to the reaction density for the special case in which [Formula: see text] and [Formula: see text] annihilate upon contact. An exact expression is found for the generating function of the mixing time. The analysis is extended to multiple reaction fronts and finitely ramified fractals. The method involves using the kernel of the Laplace transform integral operator to map and analyze a moving homogeneous Dirichlet interior point condition.
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