Geodesic
On the analytic solutions of a~special boundary value problem for a~nonlinear heat equation in polar coordinates
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 2, pp. 56-65

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The paper addresses a nonlinear heat equation (the porous medium equation) in the case of a power-law dependence of the heat conductivity coefficient on temperature. The equation is used for describing high-temperature processes, filtration of gases and fluids, groundwater infiltration, migration of biological populations, etc. The heat waves (waves of filtration) with a finite velocity of propagation over a cold background form an important class of solutions to the equation under consideration. A special boundary value problem having solutions of such type is studied. The boundary condition of the problem is given on a sufficiently smooth closed curve with variable geometry. The new theorem of existence and uniqueness of the analytic solution is proved.
Keywords: nonlinear heat equation, power series, existence and uniqueness theorem.
Mots-clés : convergence 
@article{SJIM_2018_21_2_a4,
     author = {A. L. Kazakov and P. A. Kuznetsov},
     title = {On the analytic solutions of a~special boundary value problem for a~nonlinear heat equation in polar coordinates},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {56--65},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_2_a4/}
}
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A. L. Kazakov; P. A. Kuznetsov. On the analytic solutions of a~special boundary value problem for a~nonlinear heat equation in polar coordinates. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 2, pp. 56-65. http://geodesic.mathdoc.fr/item/SJIM_2018_21_2_a4/