Geodesic
A~mathematical model of heat transmission in essentially nonlinear conjugate media
Matematičeskoe modelirovanie, Tome 2 (1990) no. 6, pp. 40-54.

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

Heat transmission in conjugate systems (cubes, cylinders, spheres) with travelling boundary line is investigated on the basis of the heat-conductivity nonlinear equation with a heat source obtained from the solution of an electrodynamic problem in a nonlinear medium whose dielectric penetrability depends on the field according to the law $$ \varepsilon_i=\varepsilon_{0i}-|\alpha_i|E_i^2,\qquad i=1,2. $$ The analysis carried out points out some nontrivial effects accompanying the heat transmission: the appearance of adiabatic surfaces, emergence of solition solutions and the conditions with sharpening in self-focusing media. All the considered effects are essentially defined by the values of $\alpha_i$ nonlinear parameters, nature of dependences of dielectric penetrabilities on the temperature, and the character of movement of the boundary surface. 
@article{MM_1990_2_6_a4,
     author = {L. A. Uvarova and V. K. Fedyanin},
     title = {A~mathematical model of heat transmission in essentially nonlinear conjugate media},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {40--54},
     publisher = {mathdoc},
     volume = {2},
     number = {6},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1990_2_6_a4/}
}
TY  - JOUR
AU  - L. A. Uvarova
AU  - V. K. Fedyanin
TI  - A~mathematical model of heat transmission in essentially nonlinear conjugate media
JO  - Matematičeskoe modelirovanie
PY  - 1990
SP  - 40
EP  - 54
VL  - 2
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_1990_2_6_a4/
LA  - ru
ID  - MM_1990_2_6_a4
ER  - 
%0 Journal Article
%A L. A. Uvarova
%A V. K. Fedyanin
%T A~mathematical model of heat transmission in essentially nonlinear conjugate media
%J Matematičeskoe modelirovanie
%D 1990
%P 40-54
%V 2
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_1990_2_6_a4/
%G ru
%F MM_1990_2_6_a4
L. A. Uvarova; V. K. Fedyanin. A~mathematical model of heat transmission in essentially nonlinear conjugate media. Matematičeskoe modelirovanie, Tome 2 (1990) no. 6, pp. 40-54. http://geodesic.mathdoc.fr/item/MM_1990_2_6_a4/