On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations

Abstract

We study the behavior of solutions of certain parabolic partial differential equations of the form ut = epsilon2 uxx + epsilong(u) ux + h(u) in the limit epsilon → 0+. Solutions of advection-diffusion and reaction-diffusion equations are specifically considered. These solutions possess slowly moving internal layers, the positions of which are often of physical interest. Previous studies have focused on solutions which exhibit exponential asymptotics; we broaden the class studied to include the more common algebraic asymptotics. Metastability and supersensitivity are also considered in both cases.