  The kinetics of encounter-controlled processes in growing domains is markedly
different from that in a static domain. Here, we consider the specific example
of diffusion limited coalescence and annihilation reactions in one-dimensional
space. In the static case, such reactions are among the few systems amenable to
exact solution, which can be obtained by means of a well-known method of
intervals. In the case of a uniformly growing domain, we show that a double
transformation in time and space allows one to extend this method to compute
the main quantities characterizing the spatial and temporal behavior. We show
that a sufficiently fast domain growth brings about drastic changes in the
behavior. In this case, the reactions stop prematurely, as a result of which
the survival probability of the reacting particles tends to a finite value at
long times and their spatial distribution freezes before reaching the fully
self-ordered state. We obtain exact results for the survival probability and
for key properties characterizing the degree of self-ordering induced by the
chemical reactions, i.e., the interparticle distribution function and the pair
correlation function. These results are confirmed by numerical simulations.
