一类非线性色散耗散波动方程的整体强解  

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

作　　者：杨海鸥[1] 郭秀芳[1] 于涛[1] 徐润章[1,2] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学自动化学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2009年第3期344-346,共3页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(10871055);黑龙江省自然科学基金资助项目(A2007-02;A200810)

摘　　要：研究一类从非线性弹性中纵向杆形变传播及弱线性作用下空间变换离子声波传播问题中提出的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.首先定义了位势井,借助该位势井实现对势能的控制,而后利用Galerkin方法证明了若满足一定的条件,则此问题存在整体强解.这些结果拓展了整体解存在所满足的增长性条件,并为进一步研究方程的其他性质提供了理论基础.The Dirichlet initial boundary value problem was studied for a class of nonlinear fourth order wave equations with dispersive and dissipative terms. These arise in a large range of physical phenomena including the propagation of deformation in nonlinear elastic rods, the propagation of ion acoustic waves in changing space with weakly nonlinear effects, and on a bounded domain in n-dimensional space where the sign of semilinear term Jr（u） is the same as u and satisfies certain growth conditions. First, the potential well was defined and with the aid of it, the potential energy is controlled. Then by the （;alerkin method, it was proven that if certain conditions were satisfied, the problem admits a global strong solution. The results obtained extend the conditions for the global existence of solutions, and build a theoretical foundation for further research.

关 键 词：非线性波动方程 色散 耗散 位势井 整体强解 存在性 

分 类 号：O175.26[理学—数学]