Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions
We study nonnegative solutions of two porous medium equations with nonlinear coupled boundary conditions and nonnegative nontrivial compactly supported initial data. We describe them in terms of the different parameters appearing in the problem, when solutions blow up in a finite time, and when they...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222518_v50_n1_p629_Quiros |
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todo:paper_00222518_v50_n1_p629_Quiros2023-10-03T14:29:54Z Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions Quirós, F. Rossi, J.D. Blow-up Degenerate parabolic system Fujita exponents Nonlinear boundary conditions We study nonnegative solutions of two porous medium equations with nonlinear coupled boundary conditions and nonnegative nontrivial compactly supported initial data. We describe them in terms of the different parameters appearing in the problem, when solutions blow up in a finite time, and when they exist globally in time. We find three regions, bounded by two curves. One of them is a Fujita type curve. In the first region every solution is global, in the second every nontrivial solution blows up, and in the last one both behaviours coexist. In the blow-up case we find the blow-up rates and the blow-up sets. In particular, we prove that under certain conditions the blow-up sets of the two components of the system are different. This is the first known example of a nontrivially coupled parabolic system showing such a behaviour. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00222518_v50_n1_p629_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 Degenerate parabolic system Fujita exponents Nonlinear boundary conditions |
| spellingShingle |
Blow-up Degenerate parabolic system Fujita exponents Nonlinear boundary conditions Quirós, F. Rossi, J.D. Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| topic_facet |
Blow-up Degenerate parabolic system Fujita exponents Nonlinear boundary conditions |
| description |
We study nonnegative solutions of two porous medium equations with nonlinear coupled boundary conditions and nonnegative nontrivial compactly supported initial data. We describe them in terms of the different parameters appearing in the problem, when solutions blow up in a finite time, and when they exist globally in time. We find three regions, bounded by two curves. One of them is a Fujita type curve. In the first region every solution is global, in the second every nontrivial solution blows up, and in the last one both behaviours coexist. In the blow-up case we find the blow-up rates and the blow-up sets. In particular, we prove that under certain conditions the blow-up sets of the two components of the system are different. This is the first known example of a nontrivially coupled parabolic system showing such a behaviour. |
| format |
JOUR |
| author |
Quirós, F. Rossi, J.D. |
| author_facet |
Quirós, F. Rossi, J.D. |
| author_sort |
Quirós, F. |
| title |
Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| title_short |
Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| title_full |
Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| title_fullStr |
Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| title_full_unstemmed |
Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| title_sort |
blow-up sets and fujita type curves for a degenerate parabolic system with nonlinear boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_00222518_v50_n1_p629_Quiros |
| work_keys_str_mv |
AT quirosf blowupsetsandfujitatypecurvesforadegenerateparabolicsystemwithnonlinearboundaryconditions AT rossijd blowupsetsandfujitatypecurvesforadegenerateparabolicsystemwithnonlinearboundaryconditions |
| _version_ |
1807314526565040128 |