Abstract
This paper establishes the blowup estimate near the blowup time for the heat equation $u_t = \Delta u$ with the nonlinear boundary condition $u_n = u^p$ on $\partial \Omega\times [0,T)$, where $\Omega$ is a bounded domain in $R^N$. It is proved that the blowup will not occur in the interior of the domain. The blowup rate is established under certain conditio
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