一类非线性波动方程的整体吸引子

Existence of global attractors for a nonlinear wave equation

为了更好地了解非线性波动方程解的性态,研究了一类含有混合导数项的非线性波动方程的整体吸引子的存在性问题:在引用Kuratowski测度的定义并对其基本性质进行讨论的基础上,通过渐近先验估计,证明了解半群{S(t)}t≥0在Kuratowski测度下的渐进光滑性,从而得到了这类含有混合导数项的非线性波动方程在H01(Ω)×L2(Ω)上的整体吸引子的存在性定理.

In order to finding out more characteristics of solution for nonlinear wave equation, this paper considers the existence of global attractor for the nonlinear wave equation involving the mixed differential quotient terms based on the definition of Kuratowski measure. Through proving the asymptotic smoothness of semigroup {S（t）}t≥0 under the Kuratowski measure, the theorem of existence of global attractor on H0^1 （Ω）× L^2（Ω） for the equation is obtained.