关于位势井及其对强阻尼非线性波动方程的应用  

ON POTENTIAL WELL AND APPLICATION TO STRONGLY DAMPED NONLIEAR WAVE EQUATIONS

作　　者：刘亚成 刘萍[2] 

机构地区：[1]哈尔滨工程大学应用数学系,哈尔滨150001 [2]哈尔滨师范大学数学系,哈尔滨150080

出　　处：《应用数学学报》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

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).

关 键 词：位势井 强阻尼 非线性波动方程 解的存在性 整体强解 整体弱解 初边值问题 首次 方法 深度 

分 类 号：O175[理学—数学]