Geodesic
On some exact solutions of the nonlinear heat equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 112-123

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The paper is devoted to finding invariant solutions of the nonlinear heat (filter) equation without sources or sinks in the case of one spatial variable and a power dependence of the thermal conduction coefficient on the temperature. The construction procedure is reduced to Cauchy problems for ordinary differential equations with a singularity at the highest derivative. An existence and uniqueness theorem is proved for solutions of such problems in the class of analytic functions (in the form of a converging series). An estimate is obtained for the convergence domain of this series in one particular case.
Keywords: partial differential equations, nonlinear heat (filter) equation, Cauchy problem.
Mots-clés : invariant solution 
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A. L. Kazakov; S. S. Orlov. On some exact solutions of the nonlinear heat equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 112-123. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a11/