| Summary: | 碩士 === 大同大學 === 應用數學學系(所) === 96 === Let $\triangle $ be the Laplace operator in
$n$ dimensional space. This paper studies the following the
initial-boundary value problem with localized reaction term:
\begin{align*}
u_{t}(x,t)=\Delta u(x,t)+
\frac{1}{(1-u(x,t))^{p}}+\frac{1}{(1-u(x^{*},t))^{q}},
(x,t)\in B\times(0,T),
\end{align*}
\begin{align*}
u(x,0)=u_{0}(x), \ x\in B,
\end{align*}
\begin{align*}
u(x,t)=0, \ (x,t)\in\partial B\times(0,T),
\end{align*}
where $B=\{x\in \Bbb{R}^n: \|x\|<1 \}$, $\partial B=\{x\in
\Bbb{R}^n: \|x\| =1\}$, $x^{*}\in B$, $0<p,\ q<\infty$, $T>0$,
and $u_{0}\geq 0$. The existence and quenching behavior of the
problem are studied. For the case $x^{*}=0$, the quenching rate
of solution near the quenching time is investigated.
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