Reaction-Subdiffusion Equations for the A <--> B Reaction

Abstract

We consider a simple linear reversible isomerization reaction A <--> B under subdiffusion described by continuous time random walks (CTRW). The reactants' transformations take place independently on the motion and are described by constant rates. We show that the form of the ensuing system of mesoscopic reaction-subdiffusion is somewhat unusual: the equation giving the time derivative of one reactant concentration, say A(x,t), contains the terms depending not only on Laplacian A, but also on Laplacian B, i.e. depends also on the transport operator of another reactant. Physically this is due to the fact that several transitions from A to B and back may take place at one site before the particle jumps.

References in corpus (4)

• Fractional Reaction-Diffusion Equation
• On reaction-subdiffusion equations
• Subdiffusion-limited reactions
• Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents

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• Mean Field Model of Coagulation and Annihilation Reactions in a Medium of Quenched Traps: Subdiffusion
• Application of hyperbolic scaling for calculation of reaction-subdiffusion front propagation
• Effective diffusion coefficients in reaction-diffusion systems with anomalous transport