Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer

Abstract

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.

Keywords

• сингулярно возмущенное эллиптическое уравнение
• случай кратного корня вырожденного уравнения
• асимптотическое разложение решения погранслойного типа
• трехзонный пограничный слой
• оценочная функция