一类非线性波动方程混合问题解的爆破  

Blow up of solution for a kind of mixed problem of nonlinear wave equations

作　　者：洪洁[1] 

机构地区：[1]成都电子机械高等专科学校人文社科系,四川成都610031

出　　处：《兰州理工大学学报》2004年第3期124-126,共3页Journal of Lanzhou University of Technology

摘　　要：基于Sattinger在1968提出的势井理论,通过构造不稳定集,应用凸形分析方法,简单地证明了一类非线性波动方程混合问题解的爆破性.即对于半线性波动方程utt-Δu=|u|r-1u的初边值问题,当初值属于不稳定集V时,解在L2(Ω)意义下,在有限时刻发生blow up现象.According to potential well theory advanced by Sattinger in 1968 and,by constructing a unstable set,the blow up behavior of the solution for a kind of mixed problem of nonlinear wave equations is verified readily by using the convexity method.That is,to the initial-boundary-value problem of semi-linear wave equation u_(tt)-Δu=|u|^(r-1)u,with an initial value belonging to an unstable set V,the solution will blow up under L^2(Ω) norm and at a finite moment.

关 键 词：非线性波动方程 势井 不稳定集 凸形分析方法 爆破 

分 类 号：O175.29[理学—数学]