带有非线性阻尼的非线性发展方程的时间依赖吸引子

Time-dependent global attractor of the nonlinear evolution equation with nonlinear damping

作者：刘亭亭(西北师范大学数学与统计学院)；马巧珍(西北师范大学数学与统计学院)

Author：LIU Ting-Ting(College of Mathematics and Statistics, Northwest Normal University)；MA Qiao-Zhen(College of Mathematics and Statistics, Northwest Normal University)

收稿日期：2016-09-01 年卷（期）页码：2017,54(5):917-924

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：非线性发展方程；非线性阻尼；时间依赖吸引子；压缩函数

Key words：nonlinear evolution equation; nonlinear damping; time-dependent attractor; contractive functions

基金项目：国家自然科学基金

中文摘要

本文考虑带有非线性阻尼的非线性发展方程解的长时间行为，通过时间依赖空间中的理论，利用压缩函数的方法与更多的估计技巧，证明了带有临界非线性项的非线性发展方程时间依赖吸引子的存在性。

英文摘要

In this article, we consider the long-time behavior of solutions for the nonlinear evolution equation with nonlinear damping. Within the theory of process on time-dependent spaces, by using the contractive functions and more detailed estimates, we prove the existence of the time-dependent attractor for the nonlinear evolution equation with critical nonlinearity.

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论文摘要

带有非线性阻尼的非线性发展方程的时间依赖吸引子

Time-dependent global attractor of the nonlinear evolution equation with nonlinear damping