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

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.