摘要
研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|^(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R^n为有界域,当n≥3时,1<p≤(n+2)/(n-2);当n=1,2时,1<p<∞.首先利用紧致性方法和位势井方法证明了此问题整体弱解的存在性.而后,利用位势井族方法证明了,当时间t→+∞时,此解依t的指数形式衰减于零.结果从根本上改进了已有结果.
In, this paper we study the initial-boundary value problem of damped semilinear wave equation utt-△u＋γut=｜u｜p-1u,x∈Ω,t〉0 u（x,0）=u0（x）,ut（x,0）=u1（x）,x∈Ω u｜ Ω=0,t≥0 where γ is a positive constant, Ω R^n Rn is a bounded domain, 1〈p≤n＋2/n-2 for n ≥ 3; 1 〈 p 〈∞ for n = 1, 2. First by using compactness method and potential well method we prove the global existence of weak solution. Then by introducing a family of potential wells, we prove that when time t→＋∞ the global weak solution decays to zero exponently.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第13期185-192,共8页
Mathematics in Practice and Theory
关键词
半线性波动方程
阻尼
整体存在性
衰减估计
位势井
Semilinear wave equation
damping
global existence
decay estimate
potential wells
