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

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English
Pages (from-to)	1567-1577
Number of pages	11
Journal	Differential Equations
Volume	53
Issue number	12
DOIs	https://doi.org/10.1134/S0012266117120059
State	Published - 1 Dec 2017

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

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.",

author = "Mingkang Ni and Yafei Pang and Levashova, \{N. T.\} and Nikolaeva, \{O. A.\}",

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AU - Ni, Mingkang

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AU - Levashova, N. T.

AU - Nikolaeva, O. A.

PY - 2017/12/1

Y1 - 2017/12/1

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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U2 - 10.1134/S0012266117120059

DO - 10.1134/S0012266117120059

M3 - 文章

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JO - Differential Equations

JF - Differential Equations

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ER -

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

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