Two-dimensional parabolic problem with a rapidly oscillating free term

In this paper, it is aimed to construct regularized asymptotics of the solution of a twodimensional 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 existence of a two-dimensional boundary layer. The presence in the free term as a rapidly oscillating factor leads to the inclusion in the asymptotic of the boundary layer with a rapidly oscillating nature of change. Vanishing of the derived phase of the free term leads to 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 the authors for singularly perturbed parabolic equations.


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