Internal layer intersecting the boundary of a domain in a singular advection–diffusion equation
Youcef Amirat, Youcef Amirat, Arnaud Münch · Asymptotic Analysis · 2023
We perform an asymptotic analysis with respect to the parameter [Formula: see text] of the solution of the scalar advection–diffusion equation [Formula: see text], [Formula: see text], supplemented with Dirichlet boundary conditions. For small values of ε, the solution [Formula: see text] exhibits a boundary layer of size [Formula: see text] in the neighborhood of [Formula: see text] (assuming [Formula: see text]) and an internal layer of size [Formula: see text] in the neighborhood of the characteristic starting from the point [Formula: see text]. Assuming that these layers interact each other after a finite time [Formula: see text] and using the method of matched asymptotic expansions, we construct an explicit approximation [Formula: see text] satisfying [Formula: see text]. We emphasize the additional difficulties with respect to the case M constant considered recently by the authors.