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.