佳木斯大学学报:自然科学版
佳木斯大學學報:自然科學版
가목사대학학보:자연과학판
Journal of Jiamusi University(Natural Science Edition)
2011年
5期
759-760,762
,共3页
非线性反应扩散方程%初边值问题%整体存在%爆破
非線性反應擴散方程%初邊值問題%整體存在%爆破
비선성반응확산방정%초변치문제%정체존재%폭파
nonlinear reaction-diffusion equation%initial-boundary value problem%global existence%blow-up
研究了下列非线性反应扩散方程初边值问题:{ut(x,t)=Δu(x,t)+up(x,t)+a(x)u(x,t),x∈Ω,t〉0 u(x,t)=0,x∈Ω,t〉0 u(x,0)=u0(x),x∈Ω非负解的整体存在和爆破问题.文章中利用半群方法得到解的整体存在的条件,利用特征函数方法分析了解在有限时刻爆破的条件.
研究瞭下列非線性反應擴散方程初邊值問題:{ut(x,t)=Δu(x,t)+up(x,t)+a(x)u(x,t),x∈Ω,t〉0 u(x,t)=0,x∈Ω,t〉0 u(x,0)=u0(x),x∈Ω非負解的整體存在和爆破問題.文章中利用半群方法得到解的整體存在的條件,利用特徵函數方法分析瞭解在有限時刻爆破的條件.
연구료하렬비선성반응확산방정초변치문제:{ut(x,t)=Δu(x,t)+up(x,t)+a(x)u(x,t),x∈Ω,t〉0 u(x,t)=0,x∈Ω,t〉0 u(x,0)=u0(x),x∈Ω비부해적정체존재화폭파문제.문장중이용반군방법득도해적정체존재적조건,이용특정함수방법분석료해재유한시각폭파적조건.
This paper studies the global existence and blow-up of the nonnegative solutions to the initial-boundary value problem for the nonlinear reaction-diffusion equation:{ut(x,t)=Δu(x,t)+up(x,t)+a(x)u(x,t),x∈Ω,t0 u(x,t)=0,x∈Ω,t0u(x,0)=u0(x),x∈Ω The method of semigroup was taken to investigate some conditions under which the global solutions of the above nonlinear reaction-diffusion equation exist,and use eigenfunction method to study the blow-up solutions.