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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Heat Conduction in Anisotropic Media: Nonlinear Self-adjointness and Conservation Laws

Discontinuity, Nonlinearity, and Complexity 1(3) (2012) 237--251 | DOI:10.5890/DNC.2012.06.002

Nail H. Ibragimov; Elena D. Avdonina

Laboratory “Group analysis of mathematical models in natural and engineering sciences”, Ufa State Aviation Technical University, 450000 Ufa, Russia

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Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed.


We acknowledge the financial support of the Government of Russian Federation through Resolution No.220, Agreement No. 11.G34.31.0042.


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  2. [2]  Ibragimov, N.H., (ed.) (1994), CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 1: Symmetries, exact solutions and conservation laws, CRC Press Inc, Boca Raton.
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