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Abstract:

We study a parabolic system of two non-linear reaction-diffusion equations completely coupled through source terms and with power-like diffusivity. Under adequate hypotheses on the initial data, we prove that non-simultaneous blow-up is sometimes possible; i.e., one of the components blows up while the other remains bounded. The conditions for non-simultaneous blow-up rely strongly on the diffusivity parameters and significant differences appear between the fast-diffusion and the porous medium case. Surprisingly, flat (homogeneous in space) solutions are not always a good guide to determine whether non-simultaneous blow-up is possible. © 2004 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:The role of non-linear diffusion in non-simultaneous blow-up
Autor:Brändle, C.; Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Blow-up; Non-linear diffusion; Parabolic system
Año:2005
Volumen:308
Número:1
Página de inicio:92
Página de fin:104
DOI: http://dx.doi.org/10.1016/j.jmaa.2004.11.004
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v308_n1_p92_Brandle.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v308_n1_p92_Brandle

Referencias:

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Citas:

---------- APA ----------
Brändle, C., Quirós, F. & Rossi, J.D. (2005) . The role of non-linear diffusion in non-simultaneous blow-up. Journal of Mathematical Analysis and Applications, 308(1), 92-104.
http://dx.doi.org/10.1016/j.jmaa.2004.11.004
---------- CHICAGO ----------
Brändle, C., Quirós, F., Rossi, J.D. "The role of non-linear diffusion in non-simultaneous blow-up" . Journal of Mathematical Analysis and Applications 308, no. 1 (2005) : 92-104.
http://dx.doi.org/10.1016/j.jmaa.2004.11.004
---------- MLA ----------
Brändle, C., Quirós, F., Rossi, J.D. "The role of non-linear diffusion in non-simultaneous blow-up" . Journal of Mathematical Analysis and Applications, vol. 308, no. 1, 2005, pp. 92-104.
http://dx.doi.org/10.1016/j.jmaa.2004.11.004
---------- VANCOUVER ----------
Brändle, C., Quirós, F., Rossi, J.D. The role of non-linear diffusion in non-simultaneous blow-up. J. Math. Anal. Appl. 2005;308(1):92-104.
http://dx.doi.org/10.1016/j.jmaa.2004.11.004