We analyze the limiting behavior of the densities ρA(t) and ρB(t) for the diffusion controlled chemical reaction A + B → inert. We prove that for equal initial densities ρA(0)=ρB(0) there is a change in behavior from d ≤4, where ρA(t)=ρB(t)∼ C t d 4, to d≥4, where ρA(t)=ρB(t)∼ C t as t→∞. For unequal initial densities ρA(t)(0)<ρB(0), ρA(t)∼e -C t in d=1, ρA(t)∼e-Ct/log t in d=2, ρA(t)∼e-Ct in d≥3. The term C depends on the initial densities and changes with d.
|Original language||English (US)|
|Number of pages||7|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - Sep 1 1990|
Bibliographical noteFunding Information:
Supported in part by NSF Grant DMS 89-01545. 2 Supported in part by NSF Grant DMR 89-18903.