Geodesic
Towards the differences in behaviour of solutions of linear and non-linear heat-conduction equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 52-59

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The linear and non-linear heat-conduction equations are analyzed by the previously initiated geometrical method of analyzing linear and non-linear equations in partial derivatives. The reason of the difference in behavior of solutions of equations under consideration was stated, as well as the reason of aggravation of the non-linear equation. A class of solutions of linear equations that represents the surfaces of the levels of non-linear heat-conduction equations was excluded.
Keywords: non-linear equations in partial derivatives; heat-conduction equations; exact solutions; surfaces of the level. 
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     title = {Towards the differences in behaviour of solutions of linear and non-linear heat-conduction equations},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     url = {http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a6/}
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L. I. Rubina; O. N. Ul'yanov. Towards the differences in behaviour of solutions of linear and non-linear heat-conduction equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 52-59. http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a6/