Asymptotic front behavior in an $A+B\rightarrow 2A$ reaction under subdiffusion
msra(2010)
摘要
We discuss the front propagation in the $A+B\rightarrow 2A$ reaction under
subdiffusion which is described by continuous time random walks with a
heavy-tailed power law waiting time probability density function. Using a
crossover argument, we discuss the two scaling regimes of the front
propagation: an intermediate asymptotic regime given by the front solution of
the corresponding continuous equation, and the final asymptotics, which is
fluctuation-dominated and therefore lays out of reach of the continuous scheme.
We moreover show that the continuous reaction subdiffusion equation indeed
possesses a front solution that decelerates and becomes narrow in the course of
time. This continuous description breaks down for larger times when the front
gets atomically sharp. We show that the velocity of such fronts decays in time
faster than in the continuous regime.
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关键词
probability density function,heavy tail,continuity equation,power law
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