Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations

被引：133
|
作者：
Gazizov, R. K. [1 ]
Ibragimov, N. H. [1 ,2 ]
Lukashchuk, S. Yu. [1 ]
机构：
[1] Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia
[2] Blekinge Inst Technol, Dept Math & Nat Sci, Res Ctr ALGA, Adv Lie Grp Anal, SE-37179 Karlskrona, Sweden
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2015年 / 23卷 / 1-3期
关键词：
Time-fractional Kompaneets equation; Symmetry; Nonlinear self-adjointness; Conservation law; Exact solution;
D O I：
10.1016/j.cnsns.2014.11.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Four time-fractional generalizations of the Kompaneets equation are considered. Group analysis is performed for physically relevant approximations. It is shown that all approximations have nontrivial symmetries and conservation laws. The symmetries are used for constructing group invariant solutions, whereas the conservation laws allow to find non-invariant exact solutions. (C) 2014 Elsevier B.V. All rights reserved.
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页码：153 / 163
页数：11
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