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Ferreira, R.; de Pablo, A.; Quirós, F.; Rossi, J.D. "Superfast quenching" (2004) Journal of Differential Equations. 199(1):189-209
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Abstract:

We study positive solutions of a fast diffusion equation in a bounded interval with a nonlinear Neumann boundary condition, Formulas are presented. where m< 0. Every positive solution quenches in a finite time. We prove that the quenching rate is not always the natural one given by homogeneity, but sometimes faster. We also study the quenching set, the asymptotic behaviour close to the quenching time and the possible continuation after that. © 2004 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Superfast quenching
Autor:Ferreira, R.; de Pablo, A.; Quirós, F.; Rossi, J.D.
Filiación:Departamento Matemáticas, Universidad Carlos III de Madrid, Escuela Politecnica Superior, 28911 Leganés, Spain
Departamento Matemťicas, Universidad Autonoma de Madrid, 28049 Madrid, Spain
Departamento Matemática, F.C.E. y N., UBA, 1428 Buenos Aires, Argentina
Palabras clave:Asymptotic behaviour; Fast diffusion equation; Nonlinear boundary conditions; Quenching
Año:2004
Volumen:199
Número:1
Página de inicio:189
Página de fin:209
DOI: http://dx.doi.org/10.1016/j.jde.2003.11.001
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v199_n1_p189_Ferreira

Referencias:

  • Aronson, D.G., Crandall, M.G., Peletier, L.A., Stabilization of solutions of a degenerate nonlinear diffusion problem (1982) Nonlinear Anal., 6, pp. 1001-1022
  • Bertsch, M., Bisegna, P., Blow-up of solutions of a nonlinear parabolic equation in damage mechanis (1997) Euro. Jnl. of Applied Mathematics, 8, pp. 89-123
  • Bertsch, M., Dal Passo, R., Ughi, M., Discontinuous "viscosity" solutions of a degenerate parabolic equation (1990) Trans. Amer. Math. Soc., 320, pp. 779-798
  • Chan, C.Y., Recent advances in quenching phenomena (1996) Proc. Dyn. Systems. Appl., 2, pp. 107-113
  • 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
  • Ferreira, R., Vázquez, J.L., Study of self-similarity for the fast diffusion equation (2003) Adv. Differential Equations, 8, pp. 1125-1152
  • Fila, M., Guo, J., Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition (2002) Nonlinear Anal., 48, pp. 995-1002
  • Giga, Y., Kohn, R.V., Characterizing blowup using similarity variables (1987) Indiana U. Math. J., 36, pp. 1-40
  • Herrero, M.A., Velázquez, J.J.L., Explosion de solutions d'équations paraboliques semilinéaires supercritiques (1994) C. R. Acad. Sci. Paris Sér. I Math., 319, pp. 141-145
  • Kawarada, H., On solutions of initial-boundary problem for ut = uxx + 1/(1 - u) (1974) Publ. Res. Inst. Math. Sci., 10, pp. 629-736
  • Levine, H.A., The phenomenon of quenching: A survey (1985) Trends in the Theory and Practice of Nonlinear Analysis, 110, pp. 275-286. , (Arlington, TX, 1984), North-Holland Math. Stud., North-Holland, Amsterdam
  • Levine, H.A., Quenching and beyond: A survey of rucent results (1993) Nonlinear Mathematical Problems in Industry, II, 2, pp. 501-512. , (Iwaki, 1992), GAKUTO Internat. Ser. Math. Sci. Appl., Gakkõtosho, Tokyo
  • Mancebo, F.J., Vega, J.M., A model of porous catalyst accounting for incipiently non-isothermal effecty (1999) J. Differential Equation, 121, pp. 79-110
  • Ferreira, R., de Pablo, A., Quirós, F., Rossi, J.D., On the quenching set for a fast diffusion equation Regional quenching, preprint; Rosen, G., Nonlinear heat conduction in solid H2 (1979) Phys. Rev. B, 19, pp. 2398-2399
  • 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. (2004) . Superfast quenching. Journal of Differential Equations, 199(1), 189-209.
http://dx.doi.org/10.1016/j.jde.2003.11.001
---------- CHICAGO ----------
Ferreira, R., de Pablo, A., Quirós, F., Rossi, J.D. "Superfast quenching" . Journal of Differential Equations 199, no. 1 (2004) : 189-209.
http://dx.doi.org/10.1016/j.jde.2003.11.001
---------- MLA ----------
Ferreira, R., de Pablo, A., Quirós, F., Rossi, J.D. "Superfast quenching" . Journal of Differential Equations, vol. 199, no. 1, 2004, pp. 189-209.
http://dx.doi.org/10.1016/j.jde.2003.11.001
---------- VANCOUVER ----------
Ferreira, R., de Pablo, A., Quirós, F., Rossi, J.D. Superfast quenching. J. Differ. Equ. 2004;199(1):189-209.
http://dx.doi.org/10.1016/j.jde.2003.11.001