Continuous Time Random Walks with Internal Dynamics and Subdiffusive Reaction-Diffusion Equations

Abstract

We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean field approximation.

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Cited by in corpus (7)

• Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
• Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous time random walks
• Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
• Disentangling sources of anomalous diffusion
• Pattern Formation on Networks with Reactions: A Continuous Time Random Walk Approach
• Cattaneo--type subdiffusion--reaction equation
• Nonergodicity of $d$-dimensional generalized Lévy walks and their relation to other space-time coupled models