Systematic analysis of the multivariate master equation for a reaction- diffusion system (Q759910)

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.