Blow-up sets for linear diffusion equations in one dimension
We consider the heat equation in the half-line with Dirichlet boundary data which blow up in finite time. Though the blow-up set may be any interval [0, a], a ∈ [0, ∞], depending on the Dirichlet data, we prove that the effective blow-up set, that is, the set of points x ≥ 0 where the solution behav...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00442275_v55_n2_p357_Quiros |
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todo:paper_00442275_v55_n2_p357_Quiros2023-10-03T14:51:36Z Blow-up sets for linear diffusion equations in one dimension Quirós, F. Rossi, J.D. Blow-up sets Heat equation Nonlinear boundary conditions We consider the heat equation in the half-line with Dirichlet boundary data which blow up in finite time. Though the blow-up set may be any interval [0, a], a ∈ [0, ∞], depending on the Dirichlet data, we prove that the effective blow-up set, that is, the set of points x ≥ 0 where the solution behaves like u(0, t), consists always only of the origin. As an application of our results we consider a system of two heat equations with a nontrivial nonlinear flux coupling at the boundary. We show that by prescribing the non-linearities the two components may have different blow-up sets. However, the effective blow-up sets do not depend on the coupling and coincide with the origin for both components. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00442275_v55_n2_p357_Quiros |
| 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 Heat equation Nonlinear boundary conditions |
| spellingShingle |
Blow-up sets Heat equation Nonlinear boundary conditions Quirós, F. Rossi, J.D. Blow-up sets for linear diffusion equations in one dimension |
| topic_facet |
Blow-up sets Heat equation Nonlinear boundary conditions |
| description |
We consider the heat equation in the half-line with Dirichlet boundary data which blow up in finite time. Though the blow-up set may be any interval [0, a], a ∈ [0, ∞], depending on the Dirichlet data, we prove that the effective blow-up set, that is, the set of points x ≥ 0 where the solution behaves like u(0, t), consists always only of the origin. As an application of our results we consider a system of two heat equations with a nontrivial nonlinear flux coupling at the boundary. We show that by prescribing the non-linearities the two components may have different blow-up sets. However, the effective blow-up sets do not depend on the coupling and coincide with the origin for both components. |
| format |
JOUR |
| author |
Quirós, F. Rossi, J.D. |
| author_facet |
Quirós, F. Rossi, J.D. |
| author_sort |
Quirós, F. |
| title |
Blow-up sets for linear diffusion equations in one dimension |
| title_short |
Blow-up sets for linear diffusion equations in one dimension |
| title_full |
Blow-up sets for linear diffusion equations in one dimension |
| title_fullStr |
Blow-up sets for linear diffusion equations in one dimension |
| title_full_unstemmed |
Blow-up sets for linear diffusion equations in one dimension |
| title_sort |
blow-up sets for linear diffusion equations in one dimension |
| url |
http://hdl.handle.net/20.500.12110/paper_00442275_v55_n2_p357_Quiros |
| work_keys_str_mv |
AT quirosf blowupsetsforlineardiffusionequationsinonedimension AT rossijd blowupsetsforlineardiffusionequationsinonedimension |
| _version_ |
1807321029971804160 |