URN etd-0806108-091433 Statistics This thesis had been viewed 2293 times. Download 901 times. Author Yen-Huang Hsu Author's Email Address No Public. Department Math Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language English Page Count 32 Title Quenching Behavior of Parabolic Problems with Localized Reaction Term Keyword Quenching Behavior Parabolic Equations Localized Reaction Term Localized Reaction Term Parabolic Equations Quenching Behavior Abstract 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.Advisor Committee Hon-hung Terence Liu - advisor

Fuh-Gwo Wang - co-chair

none - co-chair

Files indicate access worldwide Date of Defense 2008-07-25 Date of Submission 2008-08-15