Abstract
The effect of dispersive transport in the single-species reaction-diffusion models of coagulation and annihilation is considered. This transport is modelled through a fractal-time random walk, in which the stepping-times of the walker (a typical particle) follows a renewal process characterized by a pausing time distribution proportional to a stable law at long times, , with (the fractal dimension of the time). This leads to a sublinear mean squared displacement for the particles: . The decay of the concentration of particles, A(t), is obtained for all space dimensions d, and for the whole course of the reactions. The obtained results are exact for short and long times, with the long time asymptotics for d = 1, for d = 2 and for . The effect of highly non-homogeneous space distributions of particles is also considered. It is found that a fractal segregation of dimension (with ) in the initial distribution of particles in the space leads to for d = 1, for d = 2 and for , and for . This shows a subordination phenomenon in the combination of space- and time-fractal distributions.
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