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.
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
北大核心
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)
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
nonlinear wave equations
dispersivity
dissipation
potential well
global solution
existence
family of potential wells
