移動熱源的拋物型問題之討論

Existence of the solutions for parabolic problems with a moving source

陳霈軒(Pei-hsuan Chen)

指導教授 ： 廖漢雄

大同大學/電機資訊學院/應用數學學系所/碩士(2005年)

摘要

本文探討下列非線性拋物型方程解的存在性，
[ egin{array}{c}
D frac{partial T}{partial t}(x,t)-frac{partial^2T}{partial x^2}(x,t)=delta(x-x_0)F(T(x,t)), 00,
T(x,0)=widehat{T}geq0, 00,F'(T)>0,F'(T)>0$,
$D lim_{T
ightarrowinfty}F(T)=infty$, 且 $D widehat{T}(0)=0, widehat{T}(x)
ightarrow 0$ 當 $x
ightarrow infty$。

本文研究解的爆炸行為及熱源的初始位置與移動速度對爆炸性質的影響。

關鍵字

爆炸 ； 熱源

並列摘要

This paper studies the existence and non-existence of the solution $T(x,t)$ of the nonlinear parabolic problem:
[ egin{array}{c}
D frac{partial T}{partial t}(x,t)-frac{partial^2T}{partial x^2}(x,t)=delta(x-x_0)F(T(x,t)), 00,
T(x,0)=widehat{T}geq0, 00,F'(T)>0,F'(T)>0$ and
$D lim_{T
ightarrowinfty}F(T)=infty$, and $widehat{T}(0)=0, widehat{T}(x)
ightarrow 0$ as $x
ightarrow infty$.
The blow-up behavior of the solution will be studied, the effects of the initial position and the velocity of the source
related with the blow-up properties will be given.

並列關鍵字

blow-up ； heat ； source

參考文獻

ibitem{Chan-Kang_1} C. Y. Chan and P. C. Kong,

{it A thermal explosion model},

Appl. Math. and Computation 71 (1995), 201-210.

{it The blow-up property of solutions to some diffusion equations

(1992), 313-328.