Global actions of Lie symmetries for the nonlinear heat equation

被引：4

作者：

Sepanski, Mark R. ^{[1
]}

机构：

[1] Baylor Univ, Dept Math, Waco, TX 76798 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 360卷 / 01期

关键词：

Lie symmetry; Nonlinear heat equation; Global action; PARTIAL-DIFFERENTIAL-EQUATIONS; REPRESENTATION-THEORY;

D O I：

10.1016/j.jmaa.2009.06.047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By restricting to a natural class of functions, we show that the Lie point symmetries of the nonlinear heat equation exponentiate to a global action of the corresponding Lie group. Remarkably, in most of the cases, the action turns out to be linear. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：35 / 46

页数：12

共 21 条

[11]

Knapp A. W., 1986, Princeton Mathematical Series, V36

[12]

Lie S., 1891, Vorlesungen uber differentialgleichungen mit bekannten infinitesimalen transformationen

[13]

Lie S., 1881, Arch. Math., V6, P328, DOI DOI 10.1016/0167-2789(90)90123-7

[14]

Olver PJ., 2000, Applications of Lie Groups to Differential Equations

[15]

Osviannikov L., 1978, GROUP ANAL DIFFERENT

[16]

OSVIANNIKOV LV, 1959, DOKL AKAD NAUK SSSR, V125, P492

[17]

OVSIANNIKOV LV, 1962, GRUPPOVYE SVOYSTVA D

[18]

Rogers C., 1989, NONLINEAR BOUNDARY V

[19]

Sepanski M. R., SYMMETRY ANAL UNPUB

[20] On global SL(2, R) symmetries of differential operators [J].

Sepanski, MR ;

Stanke, RJ .

JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 224 (01) :1-21

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