Internal Layers for a Singularly Perturbed Second-Order Quasilinear Differential Equation with Discontinuous Right-Hand Side

Mingkang Ni; Yafei Pang; N. T. Levashova; O. A. Nikolaeva

doi:10.1134/S0012266117120059

Internal Layers for a Singularly Perturbed Second-Order Quasilinear Differential Equation with Discontinuous Right-Hand Side

Mingkang Ni^*
, Yafei Pang
, N. T. Levashova
, O. A. Nikolaeva

^*此作品的通讯作者

数学科学学院

East China Normal University
Lomonosov Moscow State University

科研成果: 期刊稿件 › 文章 › 同行评审

22 引用（Scopus）

摘要

A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.

源语言	英语
页（从-至）	1567-1577
页数	11
期刊	Differential Equations
卷	53
期	12
DOI	https://doi.org/10.1134/S0012266117120059
出版状态	已出版 - 1 12月 2017

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10.1134/S0012266117120059

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abstract = "A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.",

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AU - Nikolaeva, O. A.

PY - 2017/12/1

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N2 - A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.

AB - A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.

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Internal Layers for a Singularly Perturbed Second-Order Quasilinear Differential Equation with Discontinuous Right-Hand Side

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