Труды Института механики им. Р.Р. Мавлютова

ISSN 2542–0380

Электронный научный журнал | Electronic Scientific Journal

Proceedings of the Mavlyutov Institute of Mechanics

Ibragimov N.H., Avdonina E.D. Constructing exact solutions to anisotropic heat conduction equations by means of conservation laws Proceedings of the Mavlyutov Institute of Mechanics. 9 (2012) 1. 88–90.

2012. Vol. 9. Issue 1, Pp. 88–90
URL: http://proc.uimech.org/uim2012.1.016,en
DOI: 10.21662/uim2012.1.016

Constructing exact solutions to anisotropic heat conduction equations by means of conservation laws

Ibragimov N.H., Avdonina E.D.

The laboratory «Group analysis of mathematical models in natural and engineering sciences», Ufa State Aviation Technical University

Abstract

Recently the new theorem about conservation laws was proved by N.H. Ibragimov related to the nonlinear self-adjointness definition, and a method of exact solution construction was proposed. In the next paper by the authors, the conservation laws for anisotropic heat conduction equations were constructed. In this work the proposed method is applied to anisotropic heat equations with a source and new exact solutions are constructed.

This work was supported by the grant of the Ministry of Education and Science of the Russian Federation (contract No. 11.G34.31.0042)