Enhancement of combustion by drift in a coupled reaction-diffusion model (Q2496612)

The goal of the paper is to study reaction enhancement within a framework of a model given by a coupled sytem of 1D advection-reaction-diffusion equations \[ (T_j)_t+ A_j(T_j)_x- (T_j)_{xx}= T_j(1- T_j)+ \alpha(T_{j-1}- T_j)+ \alpha(T_{j+1}- T_j), \] \(j= 1,\dots, N\). The initial data assumed to be satisfies \(0\leq T_j(x,0)\leq 1\). The authors mainly interested in the case of the large coefficients \(A_j\), where the influence of the drift is most pronounced. They consider the front-like initial data where \(T_j(x,0)\to 0\) as \(x\to\infty\) and \(G_j(x,0)\to 1\) as \(x\to-\infty\) exponentially fast. The main result of the authors gives lower obund for the speed of propagation that are linear in the drift coefficient. The numerical experiments discussed in the paper show very good qualitative agreement with obtained rigorous result.