Nontrivial compact blow-up sets of smaller dimension

We provide examples of solutions to parabolic problems with non- trivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, ut = (um)xx + uyy + u m or ut = (|ux|p-2u x)x + uyy + up-1.For...

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Autores principales: Perez-Llanos, M., Rossi, J.D.
Formato: JOUR
Materias:
Blow-up sets
P-laplacian
Porous media
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v136_n2_p593_PerezLlanos
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00029939_v136_n2_p593_PerezLlanos
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spelling todo:paper_00029939_v136_n2_p593_PerezLlanos2023-10-03T13:55:10Z Nontrivial compact blow-up sets of smaller dimension Perez-Llanos, M. Rossi, J.D. Blow-up sets P-laplacian Porous media We provide examples of solutions to parabolic problems with non- trivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, ut = (um)xx + uyy + u m or ut = (|ux|p-2u x)x + uyy + up-1.For both equations, we prove that there exists a solution that blows up in the segment B(u) = [-L, L] ×{0}⊂ ℝ2. © 2007 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v136_n2_p593_PerezLlanos
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Blow-up sets
P-laplacian
Porous media
spellingShingle Blow-up sets
P-laplacian
Porous media
Perez-Llanos, M.
Rossi, J.D.
Nontrivial compact blow-up sets of smaller dimension
topic_facet Blow-up sets
P-laplacian
Porous media
description We provide examples of solutions to parabolic problems with non- trivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, ut = (um)xx + uyy + u m or ut = (|ux|p-2u x)x + uyy + up-1.For both equations, we prove that there exists a solution that blows up in the segment B(u) = [-L, L] ×{0}⊂ ℝ2. © 2007 American Mathematical Society.
format JOUR
author Perez-Llanos, M.
Rossi, J.D.
author_facet Perez-Llanos, M.
Rossi, J.D.
author_sort Perez-Llanos, M.
title Nontrivial compact blow-up sets of smaller dimension
title_short Nontrivial compact blow-up sets of smaller dimension
title_full Nontrivial compact blow-up sets of smaller dimension
title_fullStr Nontrivial compact blow-up sets of smaller dimension
title_full_unstemmed Nontrivial compact blow-up sets of smaller dimension
title_sort nontrivial compact blow-up sets of smaller dimension
url http://hdl.handle.net/20.500.12110/paper_00029939_v136_n2_p593_PerezLlanos
work_keys_str_mv AT perezllanosm nontrivialcompactblowupsetsofsmallerdimension
AT rossijd nontrivialcompactblowupsetsofsmallerdimension
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