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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1417-3875 |