Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer - Vera A. Beloshapko (Моделирование и анализ информационных систем, 2017)
Abstract. A singularly  perturbed elliptic problem with Dirichlet boundary conditions  is considered in the case of multiple roots of the degenerate equation.  A three-zone boundary layer arises in the vicinity of the  domain  boundary with a different scale of boundary-layer variables  and  a different behaviour  of the  solution  in different zones.  The  asymptotic expansion  of the  solution  being in fractional  powers of the small parameter, boundary-layer series are constructed using a non-standard algorithm. A complete asymptotic expansion  of the solution  is constructed and justified.