Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations
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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International Information and Engineering Technology Association
2003
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| LEADER | 06963caa a22007097a 4500 | ||
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| 001 | PAPER-4722 | ||
| 003 | AR-BaUEN | ||
| 005 | 20241015103526.0 | ||
| 008 | 190411s2003 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0345603484 | |
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| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Perazzo, Carlos Alberto | |
| 245 | 1 | 0 | |a Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations |
| 260 | |b International Information and Engineering Technology Association |c 2003 | ||
| 270 | 1 | 0 | |m Perazzo, C.A.; Universidad Favaloro, Solís 453, 1078 Buenos Aires, Argentina |
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| 504 | |a Buckmaster, J., Viscous sheets advancing over dry beds (1977) J. Fluid Mech., 81, pp. 735-756 | ||
| 504 | |a Mayergoyz, I.D., (1998) Nonlinear Diffusion of Electromagnetic Fields, , Academic Press, New York | ||
| 504 | |a Kath, W.L., Cohen, D.S., Waiting-time behavior in a nonlinear diffusion equation (1982) Stud. Appl. Math., 67, pp. 79-105 | ||
| 504 | |a Lacey, A.A., Ockendon, J.R., Tayler, A.B., "Waiting-time" solutions of nonlinear diffusion equation (1982) J. Appl. Math., 42, pp. 1252-1264 | ||
| 504 | |a Lacey, A.A., Initial motion of the free boundary for a nonlinear diffusion equation (1983) IMA J. Appl. Math., 31, pp. 113-119 | ||
| 504 | |a Aronson, D.G., Caffarelli, L.A., Vázquez, J.L., Interfaces with a corner point in one-dimensional porous medium flow (1985) Comm. Pure Appl. Math., 38, pp. 375-404 | ||
| 504 | |a Thomas, L.P., Diez, J.A., Marino, B., Gratton, R., Gratton, J., Corrientes viscogravitatorias con frentes que esperan (1991) Anales AFA, 3, pp. 213-216 | ||
| 504 | |a Gratton, J., Rossello, E., Diez, J., Physical modeling of free flow: Waiting-time behavior (1992) Mon. Ac. Nac. Ciencias Exactas Fís. y Nat, 8, pp. 51-63 | ||
| 504 | |a Marino, B.M., Thomas, L.P., Gratton, R., Diez, J.A., Betelú, S., Gratton, J., Waiting time solutions of a nonlinear diffusion equation: Experimental study of a creeping flow near a waiting front (1996) Phys. Rev. E, 54, pp. 2628-2636 | ||
| 504 | |a Gratton, J., Vigo, C.L.M., Evolution of self-similarity, and other properties of waiting-time solutions of the porous medium equation: The case of viscous gravity currents (1998) European J. Appl. Math., 9, pp. 327-350 | ||
| 504 | |a Perazzo, C.A., Vigo, C.L.M., Gratton, J., Soluciones con tiempo de espera para flujos gaseosos isotermos en un medio poroso: II Asintótica cerca del arranque (1997) Anales AFA, 9, pp. 107-110 | ||
| 504 | |a Perazzo, C.A., Vigo, C.L.M., Gratton, J., Estudio numérico de soluciones con tiempo de espera de ecuaciones no lineales de difusión (1997) Anales AFA, 9, pp. 99-103 | ||
| 504 | |a Vázquez, J.L., The interface of one-dimensional flows in porous media (1984) Trans. Amer. Math. Soc., 285, pp. 717-737 | ||
| 504 | |a Barenblatt, G.I., (1979) Similarity, Self-Similarity and Inter-me-diate Asymptotics, , Consultant Bureau, New York and London | ||
| 504 | |a Aronson, D.G., Caffarelli, L.A., Kamin, S., How an initially stationary interface begins to move in porous medium flow (1983) SIAM J. Math. Anal., 14, pp. 639-658 | ||
| 504 | |a Barenblatt, G.I., Zel'dovich, Ya.B., Self-similar solutions as intermediate asymptotics (1972) Ann. Rev. Fluid Mech., 4, pp. 295-312 | ||
| 504 | |a Gratton, J., Minotti, F., Self-similar viscous gravity currents: Phase plane formalism (1990) J. Fluid Mech., 210, pp. 155-182 | ||
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Universidad Favaloro, Solís 453, 1078 Buenos Aires, Argentina | ||
| 593 | |a INFIP-CONICET, FCEN, Universidad de Buenos Aires, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a ASYMPTOTIC STABILITY |
| 690 | 1 | 0 | |a IONIZATION OF GASES |
| 690 | 1 | 0 | |a NONLINEAR EQUATIONS |
| 690 | 1 | 0 | |a NUMERICAL METHODS |
| 690 | 1 | 0 | |a POROUS MATERIALS |
| 690 | 1 | 0 | |a PROBLEM SOLVING |
| 690 | 1 | 0 | |a THERMAL GRADIENTS |
| 690 | 1 | 0 | |a FINITE PROPAGATION VELOCITY |
| 690 | 1 | 0 | |a NONLINEAR DIFFUSION EQUATIONS |
| 690 | 1 | 0 | |a THERMAL WAVE |
| 690 | 1 | 0 | |a HEAT CONDUCTION |
| 700 | 1 | |a Vigo, C.L.M. | |
| 700 | 1 | |a Gratton, J. | |
| 773 | 0 | |d International Information and Engineering Technology Association, 2003 |g v. 21 |h pp. 121-127 |k n. 1 |p Int. J. Heat Technol. |x 03928764 |t International Journal of Heat and Technology | |
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| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p121_Perazzo |x handle |y Handle |
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| 961 | |a paper_03928764_v21_n1_p121_Perazzo |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||