Two-dimensional parabolic problem with a rapidly oscillating free term

Year 2019, Volume: 7 Issue: 1, 52 - 59, 18.06.2019

Ella Abylaeva Asan Omuraliev

Abstract

The
aim of this paper is to construct regularized asymptotics of the solution of a two-dimensional partial differential equation of parabolic
type with a small parameter for all spatial derivatives and a rapidly
oscillating free term.

     The case
when the first derivative of the phase of the free term at the initial point vanishes
is considered. The two-dimensionality of the equation leads to the
emergence of a two-dimensional boundary layer. The presence in the free term of
a rapidly oscillating factor leads to the inclusion in the asymptotic of the
boundary layer with a rapidly oscillating nature of change.  The vanishing of the derived phase of the free term
introduces into the asymptotic of a new type of boundary layer function. A
complete asymptotic solution of the problem is constructed by the method of
regularization of singularly perturbed problems developed by S.А. Lomov and
adapted by one of the authors for singularly perturbed parabolic equations.

Keywords

Asymptotics, singularly perturbed parabolic problem, oscillating free term

References

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