No abstract

The aim of the research is to develop the regularization method. By Lomov’s regularization method, we constructed a uniform asymptotic solution of the singularly perturbed Cauchy problem for a parabolic equation in the case of violation of stability conditions of the limit-operator spectrum. The problem with a “simple” turning point is considered in the case, when the eigenvalue vanishes at t=0 and has the form tm/na(t). The asymptotic convergence of the regularized series is proved.

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.

This study examines the impact of food counter‑sanctions introduced in 2014 and the accompanying shock price hike on consumer spending in Russian households. Moscow residents were studied separately as being mostly inclined to consume imported products, for whom the real total gap with potential consumer spending was estimated at 4,600 rub. per month per family, which is 2,2 times higher than the same indicator for the regions. Importantly, for the residents of Moscow the most deviating from the scenario trajectory was the cost of dairy products, while for the residents of the regions meat products were mostly deviating. In terms of the type of settlement in which the household lives, the real effect for urban dwellers was more than 3 times higher than for rural dwellers. While for the residents of cities significant parts of the losses are those in the market for fruits and vegetables, for rural residents this market was protected from negative consequences.

В статье на основе метода регуляризации С. А. Ломова построено асимптотическое решение сингулярно возмущенной задачи Коши в случае нарушения условий стабильности спектра предельного оператора. В частности, рассмотрена задача с «простой» точкой поворота, т.е. одно собственное значение обращается в ноль при $t=0$ и имеет вид $t^{m/n}$ (предельный оператор дискретно необратим).