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Abstract:

We study the simultaneous blow-up rates of a system of two heat equations coupled through the boundary in a nonlinear way. We complete the previous known results by covering the whole range of possible parameters. © 2005 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:A complete classification of simultaneous blow-up rates
Autor:Brändle, C.; Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, F.C.E y N., UBA, (1428) Buenos Aires, Argentina
Palabras clave:Blow-up rates; Nonlinear boundary conditions; Parabolic system; Boundary conditions; Parameter estimation; Thermodynamics; Blow-up rates; Nonlinear boundary conditions; Parabolic system; Nonlinear equations
Año:2006
Volumen:19
Número:7
Página de inicio:599
Página de fin:603
DOI: http://dx.doi.org/10.1016/j.aml.2005.08.007
Título revista:Applied Mathematics Letters
Título revista abreviado:Appl Math Lett
ISSN:08939659
CODEN:AMLEE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08939659_v19_n7_p599_Brandle

Referencias:

  • Brändle, C., Quirós, F., Rossi, J.D., Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary (2005) Commun. Pure Appl. Anal., 4 (3), pp. 523-536
  • Chlebík, M., Fila, M., From critical exponents to blow-up rates for parabolic problems (1999) Rend. Mat. Appl., 19 (4), pp. 449-470
  • Friedman, A., (1964) Partial Differential Equations of Parabolic Type, , Prentice-Hall Inc. Englewood Cliffs, NJ
  • Hu, B., Yin, H.M., The profile near blowup time for solution of the heat equation with a nonlinear boundary condition (1994) Trans. Amer. Math. Soc., 346 (1), pp. 117-135
  • Pedersen, M., Lin, Z., Blow-up estimates of the positive solution of a parabolic system (2001) J. Math. Anal. Appl., 255 (2), pp. 551-563
  • Pinasco, J.P., Rossi, J.D., Simultaneous versus non-simultaneous blow-up (2000) New Zealand J. Math., 29 (1), pp. 55-59
  • Quirós, F., Rossi, J.D., Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions (2001) Indiana Univ. Math. J., 50 (1), pp. 629-654
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  • Rossi, J.D., The blow-up rate for a system of heat equations with non-trivial coupling at the boundary (1997) Math. Methods Appl. Sci., 20 (1), pp. 1-11
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  • Wang, M., Fast-slow diffusion systems with nonlinear boundary conditions (2001) Nonlinear Anal. Ser. A: Theory Methods, 46 (6), pp. 893-908
  • Wang, M., Wang, S., Quasilinear reaction-diffusion systems with nonlinear boundary conditions (1999) J. Math. Anal. Appl., 231 (1), pp. 21-33
  • Zheng, S., Liu, B., Li, F., Blow-up rate estimates for a doubly coupled reaction-diffusion system J. Math. Anal. Appl., , in press
  • Zheng, S., Song, X., Jiang, Z., Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux (2004) J. Math. Anal. Appl., 298 (1), pp. 308-324

Citas:

---------- APA ----------
Brändle, C., Quirós, F. & Rossi, J.D. (2006) . A complete classification of simultaneous blow-up rates. Applied Mathematics Letters, 19(7), 599-603.
http://dx.doi.org/10.1016/j.aml.2005.08.007
---------- CHICAGO ----------
Brändle, C., Quirós, F., Rossi, J.D. "A complete classification of simultaneous blow-up rates" . Applied Mathematics Letters 19, no. 7 (2006) : 599-603.
http://dx.doi.org/10.1016/j.aml.2005.08.007
---------- MLA ----------
Brändle, C., Quirós, F., Rossi, J.D. "A complete classification of simultaneous blow-up rates" . Applied Mathematics Letters, vol. 19, no. 7, 2006, pp. 599-603.
http://dx.doi.org/10.1016/j.aml.2005.08.007
---------- VANCOUVER ----------
Brändle, C., Quirós, F., Rossi, J.D. A complete classification of simultaneous blow-up rates. Appl Math Lett. 2006;19(7):599-603.
http://dx.doi.org/10.1016/j.aml.2005.08.007