@article{article_526408, title={Two-dimensional parabolic problem with a rapidly oscillating free term}, journal={MANAS Journal of Engineering}, volume={7}, pages={52–59}, year={2019}, author={Abylaeva, Ella and Omuraliev, Asan}, keywords={Asymptotics,singularly perturbed parabolic problem,oscillating free term}, abstract={<div style="border:none;border-top:solid #000000 1pt;padding:1pt 0cm 0cm 0cm;"> <p class="MsoNormal" style="text-align:justify;border:none;padding:0cm;"> <span lang="tr" style="font-size:12pt;" xml:lang="tr">The
aim of this paper is to construct regularized asymptotics of the solution of </span> <span lang="ky" style="font-size:12pt;" xml:lang="ky">a two-dimensional partial differential equation of parabolic
type with a small parameter for all spatial derivatives and a rapidly
oscillating free term. </span> <span lang="ky" style="font-size:12pt;" xml:lang="ky"> </span> <span lang="en-us" style="font-size:12pt;" xml:lang="en-us"> </span> </p> <p> </p> <p class="MsoNormal" style="text-align:justify;border:none;padding:0cm;"> <span lang="en-us" style="font-size:12pt;" xml:lang="en-us">     The case
when the first derivative of the phase of the free term at the initial point vanishes
is considered. </span> <span lang="en-us" style="font-size:12pt;" xml:lang="en-us"> </span> <span lang="en-us" style="font-size:12pt;" xml:lang="en-us">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. </span> <span lang="tr" style="font-size:12pt;" xml:lang="tr">  </span> <span lang="en-us" style="font-size:12pt;" xml:lang="en-us">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. </span> </p> <p> </p> </div>}, number={1}, publisher={Kyrgyz-Turkish Manas University}