Dynamics of the reaction-diffusion system A + B → 0 with input of particles

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We study dynamics of filling of an initially empty finite medium by diffusing particles A and B, which arise on the surface upon dissociation of AB molecules, impinging on it with a fixed flux density I, and desorb from it by the reaction A + B→ AB→ 0. We show that once the bulk diffusivities differ (p=Dₐ/DB<1), there exists a critical flux density Ic(p), above which the relaxation dynamics to the steady state is qualitatively changed: on time dependencies of cAs/cₑ (cₑ being the steady state concentration at t→ ∞) a maximum appears, the amplitude of which grows both with I and with DB/Dₐ ratio. In the diffusion-controlled limit I ≫ Ic at p ≪ 1 the reaction "selects" the universal laws for the particles number growth Nₐ= NB∝ t¹/⁴ and the evolution of the surface concentrations cAs∝ t⁻¹/⁴,cBs∝ t¹/⁴, which are approached by one of the two characteristic regimes with the corresponding hierarchy of the intermediate power-law asymptotics. In the first of these cAs goes through a comparatively sharp max(cAs/cₑ)∝ I¹/⁶, the amplitude of which is p-independent, in the second one cAs goes through a -like max(cAs/cₑ)∝ p⁻¹/⁴, the amplitude of which is I-independent. We demonstrate that on the main filling stage the evolution of the N(t)/ Nₑ, cAs(t)/cₑ, and cBs(t)/cₑ trajectories with changing p or J between the limiting regimes is unambiguously defined by the value of the scaling parameter K=p³/²J (J being the reduced flux density) and is described by the set of scaling laws, which we study in detail analytically and numerically.