Geodesic
The upper estimation of the nonlinear equation of thermoconductivity with changing thermoconductivity coefficient depending on the law of any degree
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1985), pp. 55-62 
V. N. Hayrapetyan; Yu. N. Hayrapetyan. The upper estimation of the nonlinear equation of thermoconductivity with changing thermoconductivity coefficient depending on the law of any degree. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1985), pp. 55-62. http://geodesic.mathdoc.fr/item/UZERU_1985_2_a9/
@article{UZERU_1985_2_a9,
     author = {V. N. Hayrapetyan and Yu. N. Hayrapetyan},
     title = {The upper estimation of the nonlinear equation of thermoconductivity with changing thermoconductivity coefficient depending on the law of any degree},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {55--62},
     year = {1985},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_1985_2_a9/}
}
TY  - JOUR
AU  - V. N. Hayrapetyan
AU  - Yu. N. Hayrapetyan
TI  - The upper estimation of the nonlinear equation of thermoconductivity with changing thermoconductivity coefficient depending on the law of any degree
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 1985
SP  - 55
EP  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZERU_1985_2_a9/
LA  - ru
ID  - UZERU_1985_2_a9
ER  - 
%0 Journal Article
%A V. N. Hayrapetyan
%A Yu. N. Hayrapetyan
%T The upper estimation of the nonlinear equation of thermoconductivity with changing thermoconductivity coefficient depending on the law of any degree
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 1985
%P 55-62
%N 2
%U http://geodesic.mathdoc.fr/item/UZERU_1985_2_a9/
%G ru
%F UZERU_1985_2_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

In the case when the coefficient of thermal conductivity (diffusion) $g$ depends on the temperature (concentration) $c$, according to the law $g(c)=Ac^n$ (here $A - const, 1$) , an upper estimate is obtained for the solution of the corresponding nonlinear parabolic equation describing the process of heat (substance) propagation. It turns out to be such that at each moment of time there is a region in which the exact solution of the equation is identically equal to zero, i.e., heat (substance) propagates with a finite speed.

[1] L. Kollatts, Funktsionalnyi analiz i vychislitelnaya matematika, Mir, M., 1969 | Zbl

[2] G. V. Badalyan, “Obobschennye faktorialnye ryady”, Soobsch. In-ta matematiki i mekhaniki AN Arm. SSR, 1950, no. V, 13–84 | MR

[3] V. N. Airapetyan, Yu. N. Airapetyan, “Otsenka resheniya nelineinogo uravneniya teploprovodnosti s koeffitsientom, lineino zavisyaschim ot temperatury”, Dokl. Akad. Nauk Arm. SSR, LXXVII:1 (1983), 40–44 | Zbl

[4] V. N. Airapetyan, Yu. N. Airapetyan, “Otsenka sverkhu na reshenie nelineinogo parabolicheskogo uravneniya, imeyuschaya vid "teplovoi volny’’”, Fizika i khimiya obrabotki materialov, 1985