The regularized asymptotics of a solution of the Cauchy problem for systems of singularly perturbed ordinary differential equations is constructed. It is shown that a power boundary layer appears in such problems in addition to other boundary layers.
Строится регуляризованная асимптотика решения сингулярно возмущенной двумерной параболической задачи, когда предельный оператор не имеет спектра. В отличие от скалярной задачи, асимптотика решения двумерной задачи дополнительно содержит угловые параболические пограничные функции, которые описываются произведением параболических пограничных функций.
A regularized asymptotic expansion of the solution to a singularly perturbed two-dimensional parabolic problem in domains with boundaries containing corner points is constructed. The asymptotics of solutions to such problems contain ordinary boundary-layer functions, parabolic boundary-layer functions, and their products, which describe a corner boundary layer. -
Keywords: singularly perturbed parabolic problems parabolic boundary layer regularized asymptotics
Строится регуляризованная асимптотика решения сингулярно возмущенной двумерной параболической задачи в областях с угловыми точками границы. Асимптотика решения таких задач содержит как обыкновенные погранслойные функции, так и параболические погранслойные функции и их произведения, которые описывают угловой пограничный слой.
We examine a system of singularly perturbed parabolic equations in the case where the small parameter is involved as a coefficient of both time and spatial derivatives and the spectrum of the limit operator has a multiple zero point. In such problems, corner boundary layers appear, which can be described by products of exponential and parabolic boundary-layer functions. Under the assumption that the limit operator is a simple-structure operator, we construct a regularized asymptotics of a solution, which, in addition to corner boundary-layer functions, contains exponential and parabolic boudar ...Daha fazlası
Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı
We construct a regularized asymptotics of the solution of the first boundary value problem for a singularly perturbed two-dimensional differential equation of the parabolic type for the case in which the limit equation has a regular singularity. There arise power-law and corner boundary layers along with parabolic ones in such problems.