The role of non-linear diffusion in non-simultaneous blow-up

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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...

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Autores principales: Brändle, C., Quirós, F., Rossi, J.D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2005
Materias:
Blow-up
Non-linear diffusion
Parabolic system
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v308_n1_p92_Brandle
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_0022247X_v308_n1_p92_Brandle
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spelling paperaa:paper_0022247X_v308_n1_p92_Brandle2023-06-12T16:44:06Z The role of non-linear diffusion in non-simultaneous blow-up J. Math. Anal. Appl. 2005;308(1):92-104 Brändle, C. Quirós, F. Rossi, J.D. Blow-up Non-linear diffusion Parabolic system 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2005 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v308_n1_p92_Brandle
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Blow-up
Non-linear diffusion
Parabolic system
spellingShingle Blow-up
Non-linear diffusion
Parabolic system
Brändle, C.
Quirós, F.
Rossi, J.D.
The role of non-linear diffusion in non-simultaneous blow-up
topic_facet Blow-up
Non-linear diffusion
Parabolic system
description 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.
format Artículo
Artículo
publishedVersion
author Brändle, C.
Quirós, F.
Rossi, J.D.
author_facet Brändle, C.
Quirós, F.
Rossi, J.D.
author_sort Brändle, C.
title The role of non-linear diffusion in non-simultaneous blow-up
title_short The role of non-linear diffusion in non-simultaneous blow-up
title_full The role of non-linear diffusion in non-simultaneous blow-up
title_fullStr The role of non-linear diffusion in non-simultaneous blow-up
title_full_unstemmed The role of non-linear diffusion in non-simultaneous blow-up
title_sort role of non-linear diffusion in non-simultaneous blow-up
publishDate 2005
url http://hdl.handle.net/20.500.12110/paper_0022247X_v308_n1_p92_Brandle
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