Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations

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Heat conduction by electrons in plasmas and by radiation in partially and fully ionized gases as well as other phenomena like flows in porous media, viscous-gravity currents, etc. obey nonlinear diffusion equations and are characterized by a finite propagation velocity. Under certain conditions the...

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Autores principales: Perazzo, C.A., Vigo, C.L.M., Gratton, J.
Formato: JOUR
Materias:
Asymptotic stability
Ionization of gases
Nonlinear equations
Numerical methods
Porous materials
Problem solving
Thermal gradients
Finite propagation velocity
Nonlinear diffusion equations
Thermal wave
Heat conduction
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p121_Perazzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03928764_v21_n1_p121_Perazzo2023-10-03T15:33:54Z Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations Perazzo, C.A. Vigo, C.L.M. Gratton, J. Asymptotic stability Ionization of gases Nonlinear equations Numerical methods Porous materials Problem solving Thermal gradients Finite propagation velocity Nonlinear diffusion equations Thermal wave Heat conduction Heat conduction by electrons in plasmas and by radiation in partially and fully ionized gases as well as other phenomena like flows in porous media, viscous-gravity currents, etc. obey nonlinear diffusion equations and are characterized by a finite propagation velocity. Under certain conditions the waiting-time phenomenon occurs, consisting of a lapse in which the front of the thermal wave sits motionless, while its profile changes and a moving corner layer (a small region where the temperature gradient varies rapidly) develops. Previously we solved numerically the nonlinear diffusion equation for power law initial profiles and investigated the dependence of the waiting time on the initial conditions and the nonlinearity parameter. Here we analyze the evolution and motion of the corner layer. We find that the corner layer velocity on arriving at the front coincides with the front velocity at start-up. We investigate the intermediate asymptotics close to the front and near start-up. We detect two self-similar regimes. The first one is a constant velocity traveling wave that appears in a domain close to the corner layer. The second is a different type of self-similarity and occurs behind the corner layer but a little farther from it than the first regime. Fil:Perazzo, C.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Vigo, C.L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gratton, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p121_Perazzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic stability
Ionization of gases
Nonlinear equations
Numerical methods
Porous materials
Problem solving
Thermal gradients
Finite propagation velocity
Nonlinear diffusion equations
Thermal wave
Heat conduction
spellingShingle Asymptotic stability
Ionization of gases
Nonlinear equations
Numerical methods
Porous materials
Problem solving
Thermal gradients
Finite propagation velocity
Nonlinear diffusion equations
Thermal wave
Heat conduction
Perazzo, C.A.
Vigo, C.L.M.
Gratton, J.
Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
topic_facet Asymptotic stability
Ionization of gases
Nonlinear equations
Numerical methods
Porous materials
Problem solving
Thermal gradients
Finite propagation velocity
Nonlinear diffusion equations
Thermal wave
Heat conduction
description Heat conduction by electrons in plasmas and by radiation in partially and fully ionized gases as well as other phenomena like flows in porous media, viscous-gravity currents, etc. obey nonlinear diffusion equations and are characterized by a finite propagation velocity. Under certain conditions the waiting-time phenomenon occurs, consisting of a lapse in which the front of the thermal wave sits motionless, while its profile changes and a moving corner layer (a small region where the temperature gradient varies rapidly) develops. Previously we solved numerically the nonlinear diffusion equation for power law initial profiles and investigated the dependence of the waiting time on the initial conditions and the nonlinearity parameter. Here we analyze the evolution and motion of the corner layer. We find that the corner layer velocity on arriving at the front coincides with the front velocity at start-up. We investigate the intermediate asymptotics close to the front and near start-up. We detect two self-similar regimes. The first one is a constant velocity traveling wave that appears in a domain close to the corner layer. The second is a different type of self-similarity and occurs behind the corner layer but a little farther from it than the first regime.
format JOUR
author Perazzo, C.A.
Vigo, C.L.M.
Gratton, J.
author_facet Perazzo, C.A.
Vigo, C.L.M.
Gratton, J.
author_sort Perazzo, C.A.
title Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
title_short Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
title_full Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
title_fullStr Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
title_full_unstemmed Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
title_sort corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
url http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p121_Perazzo
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