| Summary: | 碩士 === 大同大學 === 應用數學學系(所) === 93 === 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)), 0<x<infty, t>0,
T(x,0)=widehat{T}geq0, 0<x<infty,
T(0,t)=0,
end{array} ]
where $delta(x-x_0) $ is the Dirac delta distribution, $F(T)$ is a given function with $F(T)>0,F'(T)>0,F'(T)>0$ 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.
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