Asymptotic analysis and domain decomposition for a singularly perturbed reaction–convection–diffusion system with shock–interior layer interactions

We study an initial-boundary value problem for a singularly perturbed reaction–convection–diffusion system. Asymptotic analysis is used to construct a domain decomposition method for the system to describe the asymptotic nature of the interactions between the boundary layers, interior layers and shock layers. Our results show that the formation of boundary layers and shock layers depends upon initial and boundary data. Impinging shock can thicken interior layers at the point of intersection.