---

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

Download Full Text PDF

 

Abstract

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.

Acknowledgments

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

References

1. [1]

   Galaktionov, V.A., Dorodnitsyn, V.A., Elenin, G.G., Kurdyumov, S.P. and Samarskii, A.A. (1988), A quasilinear heat equation with a source: peaking, localization, symmetry, exact solutions, asymptotics, structures, Itogi Nauki i Tekhniki, Seriya Sovremennie problemy matematiki: Noveishye dostizhenia, 28 (1986) 95-206. English transl., Journal of Soviet Mathematics, 41, 1222-1332.

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.

3. [3]	Ibragimov, N.H. (2010-2011) Nonlinear self-adjointness in constructing conservation laws, Arch. ALGA 7/8 , 1-99. See also arXiv:1109.1728v1[math-ph] (2011) 1-104.