Solvable aggregation model with monomer annihilation

We propose a simple model in which irreversible aggregations occur between any two clusters of the same species and monomer annihilations occur between any two clusters of different species. We investigate the mean-field rate equation to analyze kinetics of the system under symmetrical initial conditions. In the constant-reaction-rate case, the cluster-mass distribution of either species approaches a conventional scaling form and both species survive finally; while for the system with a fast rate kernel, both species scale according to a modified form and no species can survive at the end.