Critical exponents for a semilinear parabolic equation with variable reaction
We study the blow-up phenomenon for non-negative solutions to the following parabolic problem: [equation presented] where 0 < p = min p p(x) max p = p+ is a smooth bounded function. After discussing existence and uniqueness, we characterize the critical exponents for this problem. We prove th...
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todo:paper_03082105_v142A_n5_p1027_Ferreira2023-10-03T15:22:47Z Critical exponents for a semilinear parabolic equation with variable reaction Ferreira, R. De Pablo, A. Pérez-LLanos, M. Rossi, J.D. We study the blow-up phenomenon for non-negative solutions to the following parabolic problem: [equation presented] where 0 < p = min p p(x) max p = p+ is a smooth bounded function. After discussing existence and uniqueness, we characterize the critical exponents for this problem. We prove that there are solutions with blow-up in finite time if and only if p+ > 1. When ω = ℝ N we show that if p > 1 + 2/N, then there are global non-trivial solutions, while if 1 < p p+ 1 + 2/N, then all solutions to the problem blow up in finite time. Moreover, in the case when p < 1 + 2/N < p+, there are functions p(x) such that all solutions blow up in finite time and functions p(x) such that the problem possesses global non-trivial solutions. When ω is a bounded domain we prove that there are functions p(x) and domains ω such that all solutions to the problem blow up in finite time. On the other hand, if ω is small enough, then the problem possesses global non-trivial solutions regardless of the size of p(x). © 2012 Royal Society of Edinburgh. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03082105_v142A_n5_p1027_Ferreira |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
We study the blow-up phenomenon for non-negative solutions to the following parabolic problem: [equation presented] where 0 < p = min p p(x) max p = p+ is a smooth bounded function. After discussing existence and uniqueness, we characterize the critical exponents for this problem. We prove that there are solutions with blow-up in finite time if and only if p+ > 1. When ω = ℝ N we show that if p > 1 + 2/N, then there are global non-trivial solutions, while if 1 < p p+ 1 + 2/N, then all solutions to the problem blow up in finite time. Moreover, in the case when p < 1 + 2/N < p+, there are functions p(x) such that all solutions blow up in finite time and functions p(x) such that the problem possesses global non-trivial solutions. When ω is a bounded domain we prove that there are functions p(x) and domains ω such that all solutions to the problem blow up in finite time. On the other hand, if ω is small enough, then the problem possesses global non-trivial solutions regardless of the size of p(x). © 2012 Royal Society of Edinburgh. |
| format |
JOUR |
| author |
Ferreira, R. De Pablo, A. Pérez-LLanos, M. Rossi, J.D. |
| spellingShingle |
Ferreira, R. De Pablo, A. Pérez-LLanos, M. Rossi, J.D. Critical exponents for a semilinear parabolic equation with variable reaction |
| author_facet |
Ferreira, R. De Pablo, A. Pérez-LLanos, M. Rossi, J.D. |
| author_sort |
Ferreira, R. |
| title |
Critical exponents for a semilinear parabolic equation with variable reaction |
| title_short |
Critical exponents for a semilinear parabolic equation with variable reaction |
| title_full |
Critical exponents for a semilinear parabolic equation with variable reaction |
| title_fullStr |
Critical exponents for a semilinear parabolic equation with variable reaction |
| title_full_unstemmed |
Critical exponents for a semilinear parabolic equation with variable reaction |
| title_sort |
critical exponents for a semilinear parabolic equation with variable reaction |
| url |
http://hdl.handle.net/20.500.12110/paper_03082105_v142A_n5_p1027_Ferreira |
| work_keys_str_mv |
AT ferreirar criticalexponentsforasemilinearparabolicequationwithvariablereaction AT depabloa criticalexponentsforasemilinearparabolicequationwithvariablereaction AT perezllanosm criticalexponentsforasemilinearparabolicequationwithvariablereaction AT rossijd criticalexponentsforasemilinearparabolicequationwithvariablereaction |
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1782029490641174528 |