Geodesic
On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1057-1068

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The paper deals with a nonlinear second order parabolic PDE, which is usually called “the nonlinear heat equation”. We construct and study a particular class of solutions having the form of a heat wave that propagates on a cold (zero) background with finite velocity. The equation degenerates on the front of a heat wave and its order decreases. This fact complicates the study. We prove a new existence and uniqueness theorem for a boundary-value problem with a given heat-wave front in the class of analytical functions. Also, we are looking for exact heat-wave type solutions. The construction of these solutions is reduced to integration of the nonlinear second order ODE with singularity.
Keywords: partial differential equations, nonlinear parabolic heat equation, existence and uniqueness theorem
Mots-clés : exact solution. 
@article{SEMR_2019_16_a95,
     author = {A. L. Kazakov},
     title = {On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1057--1068},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a95/}
}
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A. L. Kazakov. On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1057-1068. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a95/