On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates

On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Industrial Mathematics Springer Journals

On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates

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Publisher
Pleiades Publishing
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Mathematics, general
ISSN
1990-4789
eISSN
1990-4797
D.O.I.
10.1134/S1990478918020060
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Applied and Industrial MathematicsSpringer Journals

Published: May 29, 2018

References

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