Combustion waves with wide reaction zones (Q1372306)

Consider the boundary value problem (*) \({d^2 \Theta \over d\xi^2}-c {d \Theta \over d\xi} +\Phi (\eta,\Theta)=0\), \(c{d\eta \over d\xi} -\Phi (\eta,\Theta) =0\), \[ -\infty< \xi <+ \infty,\;\Theta (-\infty) =\Theta_0,\;\eta(-\infty) =0,\;{d\Theta \over d\xi} (+\infty)=0, \] where \(\Phi\) is a given function describing the reaction rate and depending on some parameter \(m\). The author studies equation (*) for \(m\gg 1\) representing the case of wide reaction zones which occur when the reaction rate is significantly reduced in the course of the reaction as the product is formed. The authors show that the combustion waves have markedly different structure and velocity compared with the case of a narrow reaction zone.