Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition
In this paper, we consider a semilinear parabolic equation $$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$ with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omega\varphi(x,y) u^l(y,t)dy$ and nonnegative initial data, where $p$, $q\geq 0$ an...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2010-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=511 |
| _version_ | 1797830699247468544 |
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| author | Dengming Liu Chunlai Mu |
| author_facet | Dengming Liu Chunlai Mu |
| author_sort | Dengming Liu |
| collection | DOAJ |
| description | In this paper, we consider a semilinear parabolic equation
$$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$
with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omega\varphi(x,y) u^l(y,t)dy$ and nonnegative initial data, where $p$, $q\geq 0$ and $l>0$. The blow-up criteria and the blow-up rate are obtained. |
| first_indexed | 2024-04-09T13:40:16Z |
| format | Article |
| id | doaj.art-2dad549b616c4243ab0c528f1046fff6 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:16Z |
| publishDate | 2010-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-2dad549b616c4243ab0c528f1046fff62023-05-09T07:53:00ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752010-09-0120105111710.14232/ejqtde.2010.1.51511Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary conditionDengming Liu0Chunlai Mu1Chongqing University, Chongqing, P. R. ChinaChongqing University, Chongqing, P. R. ChinaIn this paper, we consider a semilinear parabolic equation $$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$ with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omega\varphi(x,y) u^l(y,t)dy$ and nonnegative initial data, where $p$, $q\geq 0$ and $l>0$. The blow-up criteria and the blow-up rate are obtained.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=511 |
| spellingShingle | Dengming Liu Chunlai Mu Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition Electronic Journal of Qualitative Theory of Differential Equations |
| title | Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition |
| title_full | Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition |
| title_fullStr | Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition |
| title_full_unstemmed | Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition |
| title_short | Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition |
| title_sort | blow up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=511 |
| work_keys_str_mv | AT dengmingliu blowupanalysisforasemilinearparabolicequationwithnonlinearmemoryandnonlocalnonlinearboundarycondition AT chunlaimu blowupanalysisforasemilinearparabolicequationwithnonlinearmemoryandnonlocalnonlinearboundarycondition |