Nonsimultaneous quenching
We study the possibility of nonsimultaneous quenching for positive solutions of a coupled system of two semilinear heat equations, ut = uxx - v-p, vt = vxx - u-q, p, q > 0, with homogeneous Neumann boundary conditions and positive initial data. Under some assumptions on the initial data, we p...
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todo:paper_08939659_v15_n3_p265_DePablo2023-10-03T15:41:51Z Nonsimultaneous quenching De Pablo, A. Quirós, F. Rossi, J.D. Quenching Semilinear parabolic system We study the possibility of nonsimultaneous quenching for positive solutions of a coupled system of two semilinear heat equations, ut = uxx - v-p, vt = vxx - u-q, p, q > 0, with homogeneous Neumann boundary conditions and positive initial data. Under some assumptions on the initial data, we prove that if p,q ≥ 1, then quenching is always simultaneous, if p < 1 or q < 1, then there exists a wide class of initial data with nonsimultaneous quenching, and finally, if p < 1 ≤ q or q < 1 ≤ p, then quenching is always nonsimultaneous. We also give the quenching rates in all cases. © 2002 Elsevier Science Ltd. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_08939659_v15_n3_p265_DePablo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Quenching Semilinear parabolic system |
| spellingShingle |
Quenching Semilinear parabolic system De Pablo, A. Quirós, F. Rossi, J.D. Nonsimultaneous quenching |
| topic_facet |
Quenching Semilinear parabolic system |
| description |
We study the possibility of nonsimultaneous quenching for positive solutions of a coupled system of two semilinear heat equations, ut = uxx - v-p, vt = vxx - u-q, p, q > 0, with homogeneous Neumann boundary conditions and positive initial data. Under some assumptions on the initial data, we prove that if p,q ≥ 1, then quenching is always simultaneous, if p < 1 or q < 1, then there exists a wide class of initial data with nonsimultaneous quenching, and finally, if p < 1 ≤ q or q < 1 ≤ p, then quenching is always nonsimultaneous. We also give the quenching rates in all cases. © 2002 Elsevier Science Ltd. All rights reserved. |
| format |
JOUR |
| author |
De Pablo, A. Quirós, F. Rossi, J.D. |
| author_facet |
De Pablo, A. Quirós, F. Rossi, J.D. |
| author_sort |
De Pablo, A. |
| title |
Nonsimultaneous quenching |
| title_short |
Nonsimultaneous quenching |
| title_full |
Nonsimultaneous quenching |
| title_fullStr |
Nonsimultaneous quenching |
| title_full_unstemmed |
Nonsimultaneous quenching |
| title_sort |
nonsimultaneous quenching |
| url |
http://hdl.handle.net/20.500.12110/paper_08939659_v15_n3_p265_DePablo |
| work_keys_str_mv |
AT depabloa nonsimultaneousquenching AT quirosf nonsimultaneousquenching AT rossijd nonsimultaneousquenching |
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1807324305737908224 |