Abstract:
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.
Registro:
| Documento: |
Artículo
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| Título: | Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations |
| Autor: | Perazzo, C.A.; Vigo, C.L.M.; Gratton, J. |
| Filiación: | Universidad Favaloro, Solís 453, 1078 Buenos Aires, Argentina
INFIP-CONICET, FCEN, Universidad de Buenos Aires, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
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| Palabras clave: | 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 |
| Año: | 2003
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| Volumen: | 21
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| Número: | 1
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| Página de inicio: | 121
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| Página de fin: | 127
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| Título revista: | International Journal of Heat and Technology
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| Título revista abreviado: | Int. J. Heat Technol.
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| ISSN: | 03928764
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| CODEN: | HETEE
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p121_Perazzo |
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Citas:
---------- APA ----------
Perazzo, C.A., Vigo, C.L.M. & Gratton, J.
(2003)
. Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations. International Journal of Heat and Technology, 21(1), 121-127.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p121_Perazzo [ ]
---------- CHICAGO ----------
Perazzo, C.A., Vigo, C.L.M., Gratton, J.
"Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations"
. International Journal of Heat and Technology 21, no. 1
(2003) : 121-127.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p121_Perazzo [ ]
---------- MLA ----------
Perazzo, C.A., Vigo, C.L.M., Gratton, J.
"Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations"
. International Journal of Heat and Technology, vol. 21, no. 1, 2003, pp. 121-127.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p121_Perazzo [ ]
---------- VANCOUVER ----------
Perazzo, C.A., Vigo, C.L.M., Gratton, J. Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations. Int. J. Heat Technol. 2003;21(1):121-127.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p121_Perazzo [ ]
