一类具有非线性阻尼和源项的Petrovsky方程整体解的存在性与渐近性  

Existence and asymptotic behavior of global solution for a class of Petrovsky equation with nonlinear damping and source terms

作　　者：韩献军[1,2] 薛红霞[3] 

机构地区：[1]郑州大学数学系 [2]郑州轻工业学院信息与计算科学系,河南,郑州,450002 [3]郑州航空工业管理学院数理系

出　　处：《高校应用数学学报（A辑）》2008年第2期153-158,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10671182)

摘　　要：研究了一类具有非线性阻尼和源项的Petrovsky方程u_(tt)+△~2u+au_t|u_t|^(m-2)= bu|u|^(p-2)的初边值问题.在对m,p的大小关系不加任何限制的情况下,利用稳定集证明了整体解的存在性,并且得到了整体解的渐近性质.Petrovsky equation with nonlinear damping and source terms u_(tt)+Δ~2u+au_t|u_t|^(m-2)= bu|u|^(p-2) in a bounded domain is studied in this paper,where a,b>0,m,p>2.If the evolution of solution enters into the stable set,that the solution is global regardless of any relations between m and p is proved.And the asymptotic behavior of the global solution as time goes to infinity is also studied.

关 键 词：Petrovsky方程 非线性阻尼和源项 整体解 渐近性 

分 类 号：O175[理学—数学]