Studies on Asymptotics of the Solution of Parabolic Problems with Multipoint Stationary Phase

Abstract

The goal of this study is to provide regularised asymptotics of the solution of a singularly perturbed parabolic problem when the limit operator has no range and the free term oscillates fast, and the phase derivative vanishes at finite locations. Transition layers are created when the first derivative of the phase of the free term vanishes. 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.