摘要
本文研究强阻尼非线性波动方程的初边值问题其中f(u)u≥0.首先用新的方法再次得到了位势井深度d的值,并首次得到了位势井内外结构.而后用位势井方法得到了问题的整体弱解,整体强解的存在性.最后证明了位势井W及井外集合V在问题(1)-(3)的流之下的不变性.
In this paper we study the initial-boundary value problem of strongly damped nonlinear wave equations
where f(u)u ≥0. First by using new method we again obtain the value of the depth d of potential well W, in particular,obtain the structure of W and set V which is outside W. Then by using potential well method obtain the existence of global weak solutions and strong solutions.Finally we prove that both W and V are invariant under the flow of (1)-(3).
出处
《应用数学学报》
CSCD
北大核心
2004年第4期710-722,共13页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(10271034号)
哈尔滨工程大学基础研究基金(HEUF04012)资助项目
