The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.
An asymptotic solution of the linear Cauchy problem in the presence of a “weak” turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explicitly. Estimates are given for ε that characterize the behavior of singularities for ϵ→0. The asymptotic convergence of a regularized series is proven. The results are illustrated by an example. Bibliography: six titles.
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.
Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point
