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

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

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...

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Veröffentlicht in:Communications in nonlinear science & numerical simulation 2015-06, Vol.23 (1-3), p.153-163
Hauptverfasser: Gazizov, R.K., Ibragimov, N.H., Lukashchuk, S.Yu
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Conservation law
Conservation laws
Exact solution
Exact solutions
Invariants
Mathematical analysis
Mathematical models
Nonlinear self-adjointness
Nonlinearity
Symmetry
Time-fractional Kompaneets equation
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Beschreibung
Zusammenfassung: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.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2014.11.010