Reaction diffusion equation with non-local term arises as a mean field limit of the master equation
Kazuhisa Ichikawa - The Institute of Medical Science, The University of Tokyo, 4-6-1 Shirokanedai Minato-ku, Tokyo, 108-8639, Japan (email)
Abstract: 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.
Keywords: Stochastic reaction, Reaction radius, Reaction probability.
Received: March 2009; Revised: December 2009; Published: February 2011.