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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.
In this paper we construct the asymptotics of the solution of the Cauchy problem for a singularly perturbed hyperbolic system by using the regularization method for singularly perturbed problems of S.A. Lomov. The regularization method for singularly perturbed problems of S.A. Lomov is used for the first time to construct the asymptotic solution of a hyperbolic system.
The regularized asymptotics of the solution of the first boundary-value problem for a two-dimensional differential equation of parabolic type is constructed in the case where the phase derivative vanishes at a single point. It is shown that angular and multidimensional boundary-layer functions appear in problems of this kind parallel with other types of boundary layers.
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.
Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı
The work is devoted to the construction of the asymptotics of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains, along with parabolic boundary layer functions, and power boundary layer functions.