一类非线性非自治可伸缩板方程的一致吸引子

讨论了一类带有初值条件和固定边界条件的非线性非自治可伸缩板方程u_(tt)+△~2u+αu-△u_(tt)-M(||▽u||~2)△u-γ△u_t+f(u)=σ(x,t)证明了该系统的整体适定性.进一步研究了该系统的长时间动力学,利用建立整体弱解所生成的半过程一致渐近紧性,得到了有界区域Ω■R~n(n≥1)或无界开集中一致吸引子的存在性.

Uniform Attractors for a Nonlinear Non-autonomous Extensible Plate Equation

This paper is concerned with a nonlinear non-autonomous extensible plate equation \begin{align u_{tt +\Delta^2u+\alpha u-\Delta u_{tt -M(\|\nabla u\|^2)\Delta u-\gamma\Delta u_t+f(u)=\sigma(x,t) \nonumber \end{align together with initial conditions and clamped boundary conditions. The global well-posedness of the system is proved. Moreover, the author studies the long-time dynamics of the problem and obtains the existence of uniform attractors in a bounded domain $\Omega\subseteq{\mathbb{R ^n(n\geq1)$ or in an unbounded open set by establishing the uniformly asymptotic compactness of the semi-process generated by the global weak solutions.