论文标题
在进化问题中的自主和非自主无限吸引子
Autonomous and non-autonomous unbounded attractors in evolutionary problems
论文作者
论文摘要
如果半群的慢速无疾病，即，随着时间的流逝，它的解决方案可能会差异到无穷大，那么人们仍然可以通过无限吸引子的方法来研究其动力学，这是全球吸引者经典概念的对应物。我们继续发展该理论，由Chepyzhov和Goritskii [CG92]启动。我们提供了关于未装饰的吸引子存在的抽象结果，我们研究了这些吸引子的特性以及无限制的$ω$ - 限制设置，以缓慢的非疾病环境。我们还开发了无限吸引者理论的回溯非自主对应物。我们开发的抽象理论通过对方程式$ u_t = au + f（u）$控制的自主问题的分析来说明。特别是，使用惯性歧管方法，我们提供了无限吸引子与Lipschitz函数的图相吻合的标准，或者与Lipschitz函数的图相近以进行大型参数。
If the semigroup is slowly non-dissipative, i.e., its solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounded attractors - the counterpart of the classical notion of global attractors. We continue the development of this theory started by Chepyzhov and Goritskii [CG92]. We provide the abstract results on the unbouded attractor existence, and we study the properties of these attractors, as well as of unbounded $ω$-limit sets in slowly non-dissipative setting. We also develop the pullback non-autonomous counterpart of the unbounded attractor theory. The abstract theory that we develop is illustrated by the analysis of the autonomous problem governed by the equation $u_t = Au + f(u)$. In particular, using the inertial manifold approach, we provide the criteria under which the unbounded attractor coincides with the graph of the Lipschitz function, or becomes close to the graph of the Lipschitz function for large argument.
