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URN etd-0703106-143748 Statistics This thesis had been viewed 2406 times. Download 1392 times.
Author Sheng-Hung Chen
Author's Email Address magic.david@msa.hinet.net
Department Math
Year 2005 Semester 2
Degree Master Type of Document Master's Thesis
Language English Page Count 40
Title A STUDY ON SEMILINEAR INTEGRO-DIFFERENTIAL PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS.
Keyword
  • uniqueness
  • nonlocal boundary condition
  • integro-differential equations
  • existence
  • blow up
  • blow up
  • existence
  • integro-differential equations
  • nonlocal boundary condition
  • uniqueness
  • Abstract centerline{Large Abstract} aselineskip=1.5 aselineskip
    vspace{24pt} large Let $T$, $p$ be positive constants with
    $pgeqslant 1$, $Omega$ be a smooth bounded domain in
    $Bbb{R}^n$, $partial Omega $ be the boundary of $Omega$, and
    $Delta$ be the Laplacian. This paper studies the semilinear
    parabolic integro-differential problems with nonlocal boundary
    condition:
     egin{align*}
     u_t(t,x)-Delta u(t,x) &= left(int^{t}_{0}mid u(s,x)mid ^{p}ds
    ight)  u(t,x) in  (0,T) imes Omega,
    otag
     Bu(t,x)   &= int_{Omega}K(x,y)u(t,y)dy  in  (0,T) imes partial Omega,
     u(0,x) &= u_{0}(x), xin Omega,
    otag
    &
    end{align*}
    where $K(x,y)$ and $u_{0}(x)$ are nonnegative continuous functions
    on $Omegacup partial Omega$, and $B$ is the boundary operator
     egin{equation*}
    Buequiv alpha_{0} rac{partial u}{partial
    u}+u,
    end{equation*}
    with $alpha_0geqslant 0$, and $D rac{partial u}{partial
    u }$
    denotes the outward normal derivative of $u$ on $partialOmega $.
    The local existence and uniqueness of the solution are
    investigated. Blow-up criteria for the problem is given.
    Advisor Committee
  • Hon-hung Terence Liu - advisor
  • none - co-chair
  • none - co-chair
  • Files indicate access worldwide
    Date of Defense 2006-06-30 Date of Submission 2006-07-03


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