A STUDY ON SEMILINEAR INTEGRO-DIFFERENTIAL PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS.

• Main Authors: Sheng-Hung Chen, 陳聖鴻
• Other Authors: Hon-hung Terence Liu
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/49586892784817651291

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.