摘要
考虑如下非线性Klein-Gordon系统初边值问题解的生命跨度:utt-Δu+α2u+λuv2=0,vtt-Δu+β2v+λu2v=0(x,t)∈Ω×[0,T),这里,Ω是R3中具有光滑边界的有界域,α,β为非零实数,λ<0,T>0.得到了其解的生命跨度的上界估计,且当能量为正时得到了一个新的能量上界.
Considered the lifespan of the solution for the following nonlinear Klein-Gordon system with the initial-boundary value：
{utt-Δu＋α2u＋λuv2=0,
vtt-Δu＋β2v＋λu2v=0 （x,t）∈Ω×[0,T）,
where Ω is a bounded field in R^3 with sufficiently smooth boundary δΩ, and α,β are non-zero real numbers, λ〈0, T〉0. Some estimates for the lifespan of the solution are obtained. And a new upper bound is put forward when the initial energy is positive.
出处
《大学数学》
北大核心
2008年第4期44-48,共5页
College Mathematics
基金
湖南省自然科学基金(05jj40008)
衡阳师范学院科研项目(2004D12)
