Geodesic
Simulation of Heat Waves in An Nonlinear Anisotropic~Space
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2010), pp. 239-243

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For the first time analytical solution of the problem with boundary conditions in the non-linear anisotropic space for the quasilinear parabolic heat equation where heat conductivity tensor's components are temperature functions is obtained. This solution has show a wave type of the heat diffusion. Wave's fronts are ellipse in the anisotropic space at different time moment. Existence of the solution in wave's front and time derivative and space derivatives different orders has been analysed dependence from power of temperature which influences heat conductivity tensor's components.
Keywords: nonlinear problems, analytical methods, front of temperature indignation, additional boundary conditions, integral of thermal balance. 
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     author = {V. F. Formalyov and I. A. Selin and E. L. Kuznetcova},
     title = {Simulation of {Heat} {Waves} in {An} {Nonlinear} {Anisotropic~Space}},
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V. F. Formalyov; I. A. Selin; E. L. Kuznetcova. Simulation of Heat Waves in An Nonlinear Anisotropic~Space. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2010), pp. 239-243. http://geodesic.mathdoc.fr/item/VSGTU_2010_1_a30/