一类Boussinesq方程Cauchy问题的渐近解  

The Asymptotic Solution of the Cauchy Problem for a Generalized Boussinesq Equation

作　　者：王玲芝[1] 

机构地区：[1]涪陵师范学院数学系,重庆涪陵408003

出　　处：《四川大学学报（自然科学版）》2003年第1期7-12,共6页Journal of Sichuan University(Natural Science Edition)

摘　　要：研究了广义阻尼Boussinesq方程utt-auttxx-2butxx=-cuxxxx+uxx-p2u+β(u2)xx小初值问题的解,其中x∈R1,t>0,a>0,b>0,c>0,p≠0且β∈R1.对应于阻尼振动的情形a+c>b2,建立了方程整体解的适定性.同时推出了长时间的一个渐近解.The solution of a small initial value problem for the generalized damped Boussinesq equation utt-auttxx-2butxx=-cuxxxx+uxx-p2u+β(u2)xx was considered,where x∈R1,t>0,a>0,b>0,c>0,p≠0,and β∈R1.For the case a+c>b2 corresponding to an infinite number of damped oscillations, the wellposedness of the global solution for the equation was established.And large time asymptotics of the solution were also derived.

关 键 词：BOUSSINESQ方程 CAUCHY问题 渐近解 非线性发展方程 初值问题 适定性 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]