Self-similar evolution of the A-island-B-island system at diffusion-controlled propagation of the sharp annihilation...

We consider the problem of diffusion-controlled evolution of the A-particle island--B-particle island system in a semi-infinite medium at propagation of the sharp annihilation front A+B→0. We present an exact asymptotic solution of this problem for the general case of an arbitrary ratio of species diffusivities D. This elegant analytic solution describes self-similar evolution of the island-island system at equal particle numbers of A and B species that decay by the law N∝t(-β(D)) with a nonuniversal exponent β(D), which is determined by a self-consistent condition of the front velocity selection and varies from β(D→0)∝D(-1/2)→∞ to β(D→∞)=1/2. In the quasistatic approximation, we derive nontrivial laws of the front width growth, which define the applicability limits of the presented solution for the cases of mean field and fluctuation fronts.