On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case

被引：2

作者：

Nesterov, A. V. ^{[1
]}

机构：

[1] Russian State Social Univ, Moscow 129226, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2012年 / 52卷 / 07期

基金：

俄罗斯基础研究基金会;

关键词：

initial value problems; singular perturbations; Cauchy problem; hyperbolic systems of equations; asymptotic representation of solutions; parabolic layer;

D O I：

10.1134/S0965542512070093

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A complete asymptotic expansion of the solution to an initial value problem for a singularly perturbed system of hyperbolic equations is constructed and justified. A specific feature of the problem is that its solution has a wavelet zone in a neighborhood of which the asymptotics is described by a parabolic equation.

引用

页码：1035 / 1043

页数：9

共 6 条

[1] Asymptotics of the Solution to a Singularly Perturbed System of Parabolic Equations in the Critical Case [J].

Nesterov, A. V. ;

Shuliko, O. V. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (02) :256-263

[2]

Nesterov A. V., 2007, COMP MATH MATH PHYS+, V47, P420

[3]

NESTEROV AV, 2005, C MATH MOD AN TRAK

[4]

Rozhdestvenskii B. L., 1983, Systems of quasilinear equations and their applications to gas dynamics

[5]

Vasil'eva A. B., 1985, DIFF URAVN, P1537

[6]

Vasil'eva AB., 1978, Singularly Perturbed Equations in the Critical Case

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