论文标题
半线性拉梅系统的长期动力学
Longtime dynamics of a semilinear Lamé system
论文作者
论文摘要
本文与半线性Lamé系统的长期动态有关$$ \ partial^2_t u-μΔU-（λ +μ）\ nabla {\ rm div} u +α\ partial_t u + f（u + f（u）首先，我们建立了受到关键构造$ f（u）$的有限维度全球吸引子的存在。将$λ+μ$作为正参数$ \ varepsilon $，我们讨论限制情况的某些物理方面$ \ varepsilon \ to 0 $。然后，当$ \ varepsilon \ to 0 $时，我们在参数方面显示了吸引子的上流感官。据我们所知，以前尚未研究过对拉梅系统动力学的吸引子的分析。
This paper is concerned with longtime dynamics of semilinear Lamé systems $$ \partial^2_t u - μΔu - (λ+ μ) \nabla {\rm div} u + α\partial_t u + f(u) = 0, $$ defined in bounded domains of $\mathbb{R}^3$ with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to critical forcings $f(u)$. Writing $λ+ μ$ as a positive parameter $\varepsilon$, we discuss some physical aspects of the limit case $\varepsilon \to 0$. Then, we show the upper-semicontinuity of attractors with respect to the parameter when $\varepsilon \to 0$. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before.
