| 冯保伟.一类非线性非自治可伸缩板方程的一致吸引子[J].数学年刊A辑,2016,37(1):15~30 |
| 一类非线性非自治可伸缩板方程的一致吸引子 |
| Uniform Attractors for a Nonlinear Non-autonomous Extensible Plate Equation |
| Received:January 20, 2015 Revised:September 09, 2015 |
| DOI： |
| 中文关键词: 板方程, 适定性, 一致吸引子 |
| 英文关键词:Plate equation, Well-posedness, Uniform attractors |
| 基金项目:本文受到中央高校基本科研基金 (No.JBK150128) 的资助 |
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| 中文摘要: |
| 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
\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
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$\Omega\subseteq{\mathbb{R ^n(n\geq1)$或无界开集中一致吸引子的存在性. |
| 英文摘要: |
| 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. |
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