| Summary: | 碩士 === 大同大學 === 應用數學學系(所) === 94 === 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.
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