Instability of invariant boundary conditions of a generalized Lane-Emden equation of the second-kind

被引：11

作者：

Harley, C. ^{[1
]}

Momoniat, E. ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Computat & Appl Math, Ctr Differential Equat Continum Mech & Applicat, ZA-2050 Johannesburg, South Africa

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 198卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Lane-Emden equation; Lie group method; invariant boundary condition; phase plane analysis; stability;

D O I：

10.1016/j.amc.2007.08.077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A generator of Lie point symmetries admitted by a Lane-Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane-Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary condition y' = 0 on the line x = 0 changes with changing shape factor k. We show that for values of the shape factor k > 1 the boundary condition y' = 0 is stable on the line x = 0 while it is unstable for k <= 1. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：621 / 633

页数：13

共 22 条

[1] [Anonymous], 1995, NUMERICAL SOLUTION B
[2] [Anonymous], 1969, DIFFUSION HEAT TRANS
[3] Critical values for some non-class A geometries in thermal ignition theory
Balakrishnan, E
Swift, A
Wake, GC
[J]. MATHEMATICAL AND COMPUTER MODELLING, 1996, 24 (08) : 1 - 10
[4] The thermal explosion revisited
Barenblatt, GI
Bell, JB
Crutchfield, WY
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1998, 95 (23) : 13384 - 13386
[5] Binney J., 2008, Galactic Dynamics, V2nd ed.
[6] Bluman G. W., 1989, Symmetries and Differential Equations
[7] BONNOR WB, 1956, MNRAS, V11, P351
[8] BOZKHOV Y, 2004, NONLINEAR ANAL, V57, P773
[9] ON THE SOLUTION OF THE POISSON-BOLTZMANN EQUATION WITH APPLICATION TO THE THEORY OF THERMAL EXPLOSIONS
CHAMBRE, PL
[J]. JOURNAL OF CHEMICAL PHYSICS, 1952, 20 (11) : 1795 - 1797
[10] Chandrasekhar S., 1958, An Introduction to the Study of Stellar Structure

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