半线性拟抛物方程的整体W^(1,p)解  

Global W^(1,p) solutions of semilinear pseudoparabolic equations

作　　者：刘亚成[1] 徐润章[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2004年第3期394-396,共3页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(10271034);哈尔滨工程大学基础研究基金资助项目(HEUF04012).

摘　　要：继续研究半线性拟抛物方程的初边值问题ut-Δut=f(u),x∈Ω,t>0,u(x,0)=u0(x),x∈Ω,u｜Ω=0,t≥0.证明了:若f∈C1,f′(u)上方有界,且满足增长条件｜f′(u)｜≤A｜u｜γ+B,0≤γ<∞,n=2;0≤γ≤40(Ω),其中n=1,2时,2<p<∞;n≥3时,2<p<n,则对任一T>0,此问n-2,n≥3,u0(x)∈W1,p题存在惟一整体解u(x,t)∈W1,∞(0,T;W1,p0(Ω)).本文从实质上推广了已有结果.This study is focused on the initial boundary value problem of semilinear pseudoparabolic equations ut-Δut=f(u),x∈Ω,t>0,u(x,0)=u0(x),x∈Ω,u｜Ω=0,t≥0.It was proven that if f∈C^1,f′(u)is bounded above and satisfies the growth condition:｜f′(u)｜≤A｜u｜~γ+B,0≤γ<∞,if n=2;0≤γ≤4n-2,if n≥3,u0(x)∈W~1,p0(Ω),2<p<∞ if n=1,2,2<p<n if n≥3,then for any T>0 the problem admits a unique global solution u(x,t)∈W~1,∞(0,T;W~1,p0(Ω)).The known results which are studied by Gao Boling and Liu Yacheng are generalized in essential.

关 键 词：半线性拟抛物方程 初边值 整体W^1P解 存在性 

分 类 号：O175.26[理学—数学]