Geodesic
Modeling of heat transfer in the nonlinear anisotropic space using the analytic solution
Matematičeskoe modelirovanie, Tome 24 (2012) no. 1, pp. 46-54

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Quasi-linear parabolic equation with boundary condition of the first kind in origin of coordinates is solved for the anisotropic space where heat conductivity tensor’s components have power dependence from temperature. Analysis of the solution has show a wave type and finite speed of the diffusion of heat in the anisotropic space as opposed to infinite speed of case parabolic type linear equation. It is shown that the heat wave’s front in the anisotropic space likes ellipse in case of a plane and likes ellipsoid in case of space. The domains of power law where the solution exists have been investigated. Results are discussed.
Keywords: wave heat transfer, nonlinear anisotropic space, heat conductivity tensor, analytic solution, heat flow, heat wave, heat conductivity, nonlinear problem. 
@article{MM_2012_24_1_a3,
     author = {E. L. Kuznetsova},
     title = {Modeling of heat transfer in the nonlinear anisotropic space using the analytic solution},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {46--54},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_1_a3/}
}
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E. L. Kuznetsova. Modeling of heat transfer in the nonlinear anisotropic space using the analytic solution. Matematičeskoe modelirovanie, Tome 24 (2012) no. 1, pp. 46-54. http://geodesic.mathdoc.fr/item/MM_2012_24_1_a3/