一类非线性双曲型方程整体解的存在性和渐近性

Global existence and asymptotic behavior of solution for some nonlinear hyperbolic equation

研究了一类带有非线性耗散项的双曲型方程 u tt - ∑ n i=1 ( ? u ? x i p-2 ? u ? x i )+a|u t| q-2 u t=b|u| r-2 u 在有界闭区域内的初边值问题,通过在Sobolev空间W 1,p 0(Ω) 上构造稳定集,证明了这类问题的整体解的存在性,并利用Komornik的一个重要引理给出了整体解的渐近性态.

The initial boundary value problem for a class of hyperbolic equation with nonlinear dissipative term,namely, u tt - ∑ n i=1 ( ? u ? x i p-2 ? u ? x i )+a|u t| q-2 u t=b|u| r-2 u in a bounded domain is studied.The existence of global solution to this problem is proved by constructing a stable set in W 1,p 0(Ω), ,and the asymptotic behavior of this global solution is established through an important lemma of Komornik.