Asymptotics of the solution of parabolic problems with multipoint stationary phase

Abstract

In this paper we construct the asymptotics of the solution of the singularly perturbed parabolic problem with the stationary phase and the additive free term by using the regularization method for singularly perturbed problems. In this case, the asymptotic solution consists of regular and boundary layer terms. The boundary layer members are parabolic, power and rapidly oscillating boundary layer functions, and their products. These products are called angular boundary layer functions. Angular boundary layer functions have two components: the first is described by the product of a parabolic boundary layer function and a boundary layer function, which has a rapidly oscillating change.

Asymptotic estimations of the solution for a singularly perturbed equation with unlimited boundary conditions

“…Researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14] have developed efficient asymptotic methods for singularly perturbed problems. For sufficiently small values of the parameter, these methods make it possible to construct uniform asymptotic approximations.…”