Open AccessSingularly perturbed parabolic problem with oscillating initial condition
Author(s) -
Asan Omuraliev,
Ella Abylaeva
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1905323o
Subject(s) - mathematics , mathematical analysis , parabolic cylinder function , parabolic partial differential equation , boundary value problem , function (biology) , exponential function , boundary (topology) , boundary layer , partial differential equation , mechanics , physics , evolutionary biology , biology
The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem with an oscillating initial condition. The presence of a rapidly oscillating function in the initial condition has led to the appearance of a boundary layer function in the solution, which has the rapidly oscillating character of the change. In addition, it is shown that the asymptotics of the solution contains exponential, parabolic boundary layer functions and their products describing the angular boundary layers. Continuing the ideas of works [1, 3] a complete regularized asymptotics of the solution of the problem is constructed.