Exponential Asymptotics, the Viscid Burgers ' Equation, and Standing Wave Solutions for a Reaction‐Advection‐Diffusion Model

This paper studies various boundary value problems for nonlinear singularly perturbed evolutionary equations in a bounded spatial interval for all times t ≥0. Under appropriate hypotheses, an O (ε)‐thin monotonic profile forms that separates intervals where the solution is asymptotically constant and then moves with an exponentially slow speed toward a steady state that has an interior or endpoint layer, depending on the boundary conditions.