Artículo

Ferreira, R.; De Pablo, A.; Quirós, F.; Rossi, J.D. "On the quenching set for a fast diffusion equation: Regional quenching" (2005) Royal Society of Edinburgh - Proceedings A. 135(3):585-601
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Abstract:

We study positive solutions of a very fast diffusion equation, u t = (um-1ux)x, m < 0, in a bounded interval, 0 < x < L, with a quenching-type boundary condition at one end, u(0,t) = (T - t)1/(1-m) and a zero-flux boundary condition at the other, (um-1ux)(L,t) = 0. We prove that for m ≥ -1 regional quenching is not possible: the quenching set is either a single point or the whole interval. Conversely, if m < -1 single-point quenching is impossible, and quenching is either regional or global. For some lengths the above facts depend on the initial data. The results are obtained by studying the corresponding blow-up problem for the variable v = um-1. © 2005 The Royal Society of Edinburgh.

Registro:

Documento: Artículo
Título:On the quenching set for a fast diffusion equation: Regional quenching
Autor:Ferreira, R.; De Pablo, A.; Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, F.C.E y N., Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Año:2005
Volumen:135
Número:3
Página de inicio:585
Página de fin:601
Título revista:Royal Society of Edinburgh - Proceedings A
Título revista abreviado:R. Soc. Edinburgh Proc. A
ISSN:03082105
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira

Referencias:

  • Aronson, D., Crandall, M.G., Peletier, L.A., Stabilization of solutions of a degenerate nonlinear diffusion problem (1982) Nonlin. Analysis, 6, pp. 1001-1022
  • Bertsch, M., Ughi, M., Positivity properties of viscosity solutions of a degenerate parabolic equation (1990) Nonlin. Analysis, 14, pp. 571-592
  • Bertsch, M., Dal Passo, R., Ughi, M., Discontinuous 'viscosity' solutions of a degenerate parabolic equation (1990) Trans. Am. Math. Soc., 320, pp. 779-798
  • Bertsch, M., Dal Passo, R., Ughi, M., Nonuniqueness of solutions of a degenerate parabolic equation (1992) Annli Mat. Pura Appl., 161, pp. 57-81
  • Chan, C.Y., Recent advances in quenching phenomena (1996) Proc. Dynamic Systems and Applications, Atlanta, GA, 1995, 2, pp. 107-113. , Atlanta, GA: Dynamic
  • Chipot, M., Fila, M., Quittner, P., Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions (1991) Acta Math. Univ. Comenian., 60, pp. 35-103
  • Cortázar, C., Del Pino, M., Elgueta, M., On the blow-up set for ut = Δum + u m, m &gt; 1 (1998) Indiana Univ. Math. J., 47, pp. 541-561
  • Ferreira, R., Vazquez, J.L., Study of self-similarity for the fast diffusion equation (2003) Adv. Diff. Eqns, 8, pp. 1125-1152
  • Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D., Superfast quenching (2004) J. Diff. Eqns, 199, pp. 189-209
  • Galaktionov, V.A., Vazquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete Contin. Dynam. Syst. A, 8, pp. 399-433
  • Gilding, B.H., Herrero, M.A., Localization and blow-up of thermal waves in nonlinear heat conduction with peaking (1988) Math. Ann., 282, pp. 223-242
  • Kawarada, H., On solutions of initial-boundary problem for ut = u xx + 1/(1 - U) (1974) Publ. Res. Inst. Math. Sci., 10, pp. 729-736
  • King, J.R., Asymptotic results for nonlinear outdiffusion (1994) Bur. J. Appl. Math., 6, pp. 359-390
  • Ladyzhenskaya, O.A., Solonnikov, V.A., Ural'ceva, N.N., (1968) Linear and Quasilinear Equations of Parabolic Type., 23. , Mathematical Monographs, Providence, RI: American Mathematical Society
  • Levine, H.A., (1985) The Phenomenon of Quenching: A Survey, 110, pp. 275-286. , Trends in the theory and practice of nonlinear analysis, North-Holland Mathematics Studies Amsterdam: North-Holland
  • Levine, H.A., Quenching and beyond: A survey of recent results (1993) Nonlinear Mathematical Problems in Industry, II, 2, pp. 501-512. , GAKUTO International Series on Mathematical Science and Applications, Tokyo: Gakkötosho
  • Mancebo, F.J., Vega, J.M., A model of porous catalyst accounting for incipiently non-isothermal effecty (1999) J. Diff. Eqns, 121, pp. 79-110
  • Rodríguez, A., Vazquez, J.L., Obstructions to existence in fast-diffusion equations (2002) J. Diff. Eqns, 184, pp. 348-385
  • Rosen, G., Nonlinear heat conduction in solid H2 (1979) Phys. Rev. B, 19, pp. 2398-2399
  • Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1987) Blow-up in Problems for Quasilinear Parabolic Equations, , Moscow: Nauka, (In Russian.) English transi. Berlin: Walter de Gruyter
  • Yu, S., Tan, T.Y., Gösele, U., Diffusion mechanism of cromium in GaAs (1991) J. Appl. Phys., 70, pp. 4827-4836
  • Yu, S., Tan, T.Y., Gösele, U., Diffusion mechanism of zinc and beryllium in gallium arsenide (1991) J. Appl. Phys., 69, pp. 3547-3565

Citas:

---------- APA ----------
Ferreira, R., De Pablo, A., Quirós, F. & Rossi, J.D. (2005) . On the quenching set for a fast diffusion equation: Regional quenching. Royal Society of Edinburgh - Proceedings A, 135(3), 585-601.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]
---------- CHICAGO ----------
Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D. "On the quenching set for a fast diffusion equation: Regional quenching" . Royal Society of Edinburgh - Proceedings A 135, no. 3 (2005) : 585-601.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]
---------- MLA ----------
Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D. "On the quenching set for a fast diffusion equation: Regional quenching" . Royal Society of Edinburgh - Proceedings A, vol. 135, no. 3, 2005, pp. 585-601.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]
---------- VANCOUVER ----------
Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D. On the quenching set for a fast diffusion equation: Regional quenching. R. Soc. Edinburgh Proc. A. 2005;135(3):585-601.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]