Front propagation in A+B -> 2A reaction under subdiffusion

Abstract

We consider an irreversible autocatalytic conversion reaction A+B -> 2A under subdiffusion described by continuous time random walks. The reactants' transformations take place independently on their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation leading to the existence of a nonzero minimal front propagation velocity which is really attained by the front in its stable motion. We show that for subdiffusion this minimal propagation velocity is zero, which suggests propagation failure.

References in corpus (6)

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• On reaction-subdiffusion equations
• How to Measure Subdiffusion Parameters
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Cited by in corpus (7)

• Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
• Continuous Time Random Walks with Internal Dynamics and Subdiffusive Reaction-Diffusion Equations
• Asymptotic front behavior in an $A+B\to 2A$ reaction under subdiffusion
• Application of hyperbolic scaling for calculation of reaction-subdiffusion front propagation
• Effective diffusion coefficients in reaction-diffusion systems with anomalous transport
• Limiting Hamilton-Jacobi Equation for the Large Scale Asymptotics of a Subdiffusion Jump-Renewal Equation
• Stochastic approach to Fisher and Kolmogorov, Petrovskii, and Piskunov wave fronts for species with different diffusivities in dilute and concentrated solutions