Geodesic
About one Method of Obtaining of the Exact Analytical Decision of the Hyperbolic Equation of Heat Conductivity on the Basis of Use of Orthogonal Methods
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 159-169

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On the basis of use of a method of division of variables and an orthogonal method of Bubnov–Galyorkin the exact analytical decision of the hyperbolic equation of heat conductivity for an infinite plate under boundary conditions of the first sort is obtained. It is shown that having warmed up (or cooled)a body it is defined by movement of front of a shock thermal wave on which there is a breakage temperature curve (temperature jump). The front of a thermal wave divides investigated area on two subareas — revolted where the temperature changes from wall temperature (a boundary condition of the first sort) to the temperature at the front waves and not revolted where the temperature is equal to reference temperature.
Keywords: hyperbolic equation, analytical decision, shock thermal wave front, thermal wave speed, relaxation time. 
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     author = {V. A. Kudinov and I. V. Kudinov},
     title = {About one {Method} of {Obtaining} of the {Exact} {Analytical} {Decision} of the {Hyperbolic} {Equation} of {Heat} {Conductivity} on the {Basis} of {Use} of {Orthogonal} {Methods}},
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V. A. Kudinov; I. V. Kudinov. About one Method of Obtaining of the Exact Analytical Decision of the Hyperbolic Equation of Heat Conductivity on the Basis of Use of Orthogonal Methods. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 159-169. http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a17/