A. L. Kazakov, P. A. Kuznetsov, “On the analytic solutions of a special boundary value problem for a nonlinear heat equation in polar coordinates”, Sib. Zh. Ind. Mat., 2018, Volume 21, Number 2,Pages <nobr>56

This article is cited in 22 papers

On the analytic solutions of a special boundary value problem for a nonlinear heat equation in polar coordinates

A. L. Kazakov^a, P. A. Kuznetsov^b

^a Matrosov Institute for System Dynamics and Control Theory SB RAS, 134 Lermontova str., 664033 Irkutsk
^b Irkutsk State University, 1 K. Marx str., 664033 Irkutsk

Abstract: 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, convergence, existence and uniqueness theorem.

UDC: 517.95

Received: 25.07.2017

DOI: 10.17377/sibjim.2018.21.205