一类非线性色散耗散波动方程的整体解  

Global solutions for a class of nonlinear wave equations with dispersive-dissipative terms

作　　者：杨海鸥[1] 郭秀芳[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2008年第8期886-890,共5页Journal of Harbin Engineering University

基　　金：黑龙江省自然科学基金资助项目(A2007-02)

摘　　要：研究一类具有色散项与耗散项的四阶非线性波动方程在n维空间中有界域上的Dirichlet初边值问题.其中,半线性项f(u)与u的符号相同,并满足一定的增长条件.定义了位势井W及一族位势井,证明了若满足一定的条件,则此问题存在一个整体弱解,且此解在这族位势井中,最后证明了整体强解的存在唯一性.The Dirichlet initial boundary value problem is studied for a class of nonlinear wave equations of fourth order with dispersive and dissipative terms on a bounded domain in n-dimensional space, where the sign of semi-linear term f（u） is the same as u and satisfies certain growth conditions. First, the potential well W and a family of potential wells are defined. Then it is proven that if certain conditions are satisfied, the problem has a global weak solution which belongs to the family of potential wells. Finally, the existence and uniqueness of global strong solution to this problem were proven.

关 键 词：非线性波动方程 色散 耗散 位势井 整体解 存在性 位势井族 

分 类 号：O175.26[理学—数学]