Group classification of linear evolution equations

被引：19

作者：

Bihlo, Alexander ^{[1
]}

Popovych, Roman O. ^{[2
,3
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Wolfgang Pauli Inst, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] NAS Ukraine, Inst Math, 3 Tereshchenkivska Str, UA-01601 Kiev, Ukraine

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 448卷 / 02期

基金：

加拿大自然科学与工程研究理事会; 奥地利科学基金会;

关键词：

Group classification of differential equations; Lie symmetries; Equivalence transformations; Lie reduction; Linear evolution equations; Exact solutions; PARTIAL-DIFFERENTIAL-EQUATIONS; THIN-FILM EQUATIONS; CONSTANT-COEFFICIENTS; DIFFUSION-EQUATIONS; CONSERVATION-LAWS; SYMMETRIES; SYSTEMS; EXISTENCE; ALGEBRAS; WAVES;

D O I：

10.1016/j.jmaa.2016.11.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The group classification problem for the class of (1+1)-dimensional linear rth order evolution equations is solved for arbitrary values of r > 2. It is shown that a related maximally gauged class of homogeneous linear evolution equations is uniformly semi-normalized with respect to linear superposition of solutions and hence the complete group classification can be obtained using the algebraic method. We also compute exact solutions for equations from the class under consideration using Lie reduction and its specific generalizations for linear equations. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：982 / 1005

页数：24

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