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Title page for etd-0705105-144344


URN etd-0705105-144344 Statistics This thesis had been viewed 1394 times. Download 11 times.
Author Pei-hsuan Chen
Author's Email Address pipi89421@yahoo.com.tw
Department Math
Year 2004 Semester 2
Degree Master Type of Document Master's Thesis
Language English Page Count 31
Title Existence of the solutions for parabolic problems with a moving source
Keyword
  • source
  • heat
  • blow-up
  • blow-up
  • heat
  • source
  • Abstract 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.
    Advisor Committee
  • Hon-hung Terence Liu - advisor
  • none - co-chair
  • none - co-chair
  • Files indicate in-campus access only
    Date of Defense 2005-07-04 Date of Submission 2005-07-05


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