SHOCK-LAYER BOUNDS FOR A SINGULARLY PERTURBED EQUATION

The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equ ation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle argum ents. The bounding functions demonstrate that the size of the shock-la yer is proportional to the parameter multiplying the diffusion term.