一类非线性波动方程的整体解存在性及衰减估计  

The existence of the global solutions and energy decay estimate for a class of nonlinear wave equations

作　　者：周小燕[1] 

机构地区：[1]浙江科技学院理学院,杭州310023

出　　处：《扬州大学学报（自然科学版）》2011年第2期23-26,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：浙江省自然科学基金资助项目(Y6100016);浙江省教育厅科研基金资助项目(Y200907298)

摘　　要：研究一类非线性波动方程的整体解:首先运用乘子方法得到解的能量衰减估计,然后定义稳定集和不稳定集,根据连续性原理得到解的整体存在性,最后应用势井理论证明了解在有限时间内爆破.This paper studies the global solutions for a class of nonlinear wave equations.The energy decay rate of the global solutions is estimated by the multiplier method.The existence of the global solutions is proved by principle of continuity,the stable sets and unstable sets are defined as well.The blow-up result of the solution in finite time is also established by the ideal of a potential well theory.

关 键 词：非线性波动方程 衰减估计 整体解 存在性 爆破解 

分 类 号：O175.2[理学—数学]