Systematic analysis of the multivariate master equation for a reaction- diffusion system
type: Item
instance of: scholarly article
title: Systematic analysis of the multivariate master equation for a reaction- diffusion system
zbMATH Open document ID: 0554.35059
DOI: 10.1007/BF01012869
published in: Journal of Statistical Physics
publication date: 1980-01-01T00:00:00Z
review text: The authors investigate reaction-diffusion equations described by systems of the form \((1)\quad x_ t=v(x;\lambda)+D\Delta x,\) \(D=diagonal\) matrix. They study problem (1) by appealing to the chemical and diffusion mechanisms (random walk) which gives rise to (1). The corresponding equation is then called the master equation. They apply this analysis to a system described by the following reaction scheme: \[ A+2X\rightleftarrows^{k_ 1}_{k_ 2}3X;\quad X\rightleftarrows^{k_ 3}_{k_ 4}B. \] The master equation corresponding to this scheme is then analysed by a singular perturbation analysis. A similar analysis is then also carried out for a slightly different scheme.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 3882851
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: random walk
zbMATH Keywords: master equation
zbMATH Keywords: singular perturbation analysis
author: Gregoire Nicolis
author: M. Malek Mansour
reviewed by: Robert L. Taylor
MaRDI profile type: Publication
cites work: The Poisson representation. I: A new technique for chemical master equations
cites work: Strong approximation theorems for density dependent Markov chains
description: scientific article; zbMATH DE number 3882851