A note on boundary layer of a nonlinear evolution system with damping and diffusions

In this paper, we consider an initial-boundary value problem for a nonlinear evolution system with damping and diffusions on the strip. Our main purpose is to investigate zero-diffusion limits, which formally yield parabolic–hyperbolic coupled equations resulting from parabolic–parabolic coupled equations. It is shown that the boundary layer thickness is of the order O(βγ)O(βγ) with 0<γ<34 as the diffusion parameter β goes to zero.