Reaction diffusion equation with non-local term arises as a mean field limit of the master equation

Pages: 115 - 126, Volume 5, Issue 1, February 2012

doi:10.3934/dcdss.2012.5.115       Abstract        References        Full Text (316.0K)       Related Articles

Kazuhisa Ichikawa - The Institute of Medical Science, The University of Tokyo, 4-6-1 Shirokanedai Minato-ku, Tokyo, 108-8639, Japan (email)
Mahemauti Rouzimaimaiti - Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho, Toyonakashi, 560-8531, Japan (email)
Takashi Suzuki - Japan Science and Technology Agency, CREST 5, Sanbancho, Chiyoda-ku, Tokyo, 102-0075, 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.
Mathematics Subject Classification:  35K57, 93A30.

Received: March 2009;      Revised: December 2009;      Published: February 2011.

 References