Diffusion-controlled death of $A$-particle and $B$-particle islands at propagation of the sharp annihilation front $A + B \to 0$

Abstract

We consider the problem of diffusion-controlled evolution of the system $A$-particle island - $B$-particle island at propagation of the sharp annihilation front $A+B\to 0$. We show that this general problem, which includes as particular cases the sea-sea and the island-sea problems, demonstrates rich dynamical behavior from self-accelerating collapse of one of the islands to synchronous exponential relaxation of the both islands. We find a universal asymptotic regime of the sharp front propagation and reveal limits of its applicability for the cases of mean-field and fluctuation fronts.