Asymptotics of the Solution of Parabolic Problems with Multipoint Stationary Phase

摘要

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem when the limit operator has not range and with rapidly oscillating free term, its derivative of the phase vanishes at finite points. The vanishing of the first derivative of the phase of the free term induces transition layers. It is shown that the asymptotic solution of the problem contains parabolic, inner, corner and rapidly oscillating boundary-layer functions. Corner boundary-layer functions have two components: the first component is described by the product of parabolic boundary layer and boundary layer functions, which have a rapidly oscillating nature of the change, and the second component is described by the product of the inner and parabolic boundary layer functions.