具有强阻尼项和非线性阻尼项的波动方程解的整体存在性和有限时间爆破(英文)  

Global Solutions and Finite Time Blow Up for Wave Equations with Both Strong and Nonlinear Damping Terms

作　　者：黄文毅[1] 张健[2] 

机构地区：[1]四川大学数学学院,四川成都610064 [2]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《应用数学》2008年第4期787-793,共7页Mathematica Applicata

基　　金：National Natural Science Foudation(10771151)

摘　　要：本文考虑了一类具有强阻尼和非线性阻尼项的波动方程:utt-Δu-ωΔut+μ|ut|m-2ut=|u|p-2u,其中p>2,m>2,ω=μ=1.利用变分法和紧性引理,本文证明了基态驻波解的存在性.并且得到了解的整体存在和爆破条件.：This paper is concerned with the wave equation with strong damping and nonlinear damping terms ：utt-Δu-ωΔut＋μ｜ut｜m-2ut=｜u｜^p-2u, where p 〉 2, m 〉 2 and ω = μ = 1. Using variational calulus and compactness lemma, the existence of standing waves of the ground states is proved. Furthermore, the conditions are obtained for the global existence and finite time blow up of solutions.

关 键 词：非线性波动方程 非线性阻尼项 强阻尼项 整体存在性 爆破 

分 类 号：O175.2[理学—数学]