Geodesic
Approximate solutions to a nonlinear heat conduction problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 2044-2051

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A nonlinear heat conduction problem on a half-line is examined. It is assumed that the temperature at the medium boundary varies with time according to a power or exponential law and that the initial temperature of the medium is zero. An approximate solution to the problem is obtained. Exact solutions are found in special cases. The convergence of the solutions found is discussed. 
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     author = {N. A. Kudryashov},
     title = {Approximate solutions to a nonlinear heat conduction problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2044--2051},
     publisher = {mathdoc},
     volume = {45},
     number = {11},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a11/}
}
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N. A. Kudryashov. Approximate solutions to a nonlinear heat conduction problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 2044-2051. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a11/