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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2008
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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v136_n2_p593_PerezLlanos http://hdl.handle.net/20.500.12110/paper_00029939_v136_n2_p593_PerezLlanos |
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paper:paper_00029939_v136_n2_p593_PerezLlanos2023-06-08T14:23:29Z Nontrivial compact blow-up sets of smaller dimension 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. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v136_n2_p593_PerezLlanos 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 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. |
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 |
publishDate |
2008 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v136_n2_p593_PerezLlanos http://hdl.handle.net/20.500.12110/paper_00029939_v136_n2_p593_PerezLlanos |
_version_ |
1768545533310271488 |