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Reaction diffusion equation with non-local term arises as a mean field limit of the master equation. (English) Zbl 1364.82042

Summary: We formulate a reaction-diffusion equation with non-local term as a mean field equation of the master equation where the particle density is defined continuously in space and time. In the case of the constant mean waiting time, this limit equation is associated with the diffusion coefficient of A. Einstein, the reaction rate in phenomenology, and the Debye term under the presence of potential.

MSC:

82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
35K57 Reaction-diffusion equations
93A30 Mathematical modelling of systems (MSC2010)
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