Asymptotic analysis of an advection‐diffusion equation involving interacting boundary and internal layers
Youcef Amirat, Arnaud Münch · Mathematical Methods in the Applied Sciences · 2020
As ε goes to zero, the unique solution of the scalar advection‐diffusion equation , (x,t)∈(0,1)×(0,T) with Dirichlet boundary conditions exhibits a boundary layer of size and an internal layer of size . If the time T is large enough, these thin layers, where the solution yε displays rapid variations, intersect and interact with each other. Using the method of matched asymptotic expansions, we show how we can construct an explicit approximation of the solution yε satisfying and for all ε small enough.