Asymptotic analysis of an advection-diffusion equation and application to boundary controllability

Abstract

We perform the asymptotic analysis of the scalar advection-diffusion equation y e t −ey e xx +M y e x = 0, (x, t) ∈ (0, 1) × (0, T), with respect to the diffusion coefficient e. We use the matched asymptotic expansion method which allows to describe the boundary layers of the solution. We then use the asymptotics to discuss the controllability property of the solution for T ≥ 1/M .