带有热记忆的非均匀柔性结构的长时间动力行为

冯保伟, 李海燕

数学学报 ›› 2020, Vol. 63 ›› Issue (6) : 587-600.

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数学学报 ›› 2020, Vol. 63 ›› Issue (6) : 587-600. DOI: 10.12386/A2020sxxb0050
论文

带有热记忆的非均匀柔性结构的长时间动力行为

    冯保伟1, 李海燕2
作者信息 +

Long-time Dynamics of a Non-uniform Flexible Structure with Thermal Memory

    Bao Wei FENG1, Hai Yan LI2
Author information +
文章历史 +

摘要

本文研究了带有热效应的非均匀柔性结构方程,并且该热效应符合Coleman-Gurtin定律.利用半群方法,建立了系统的整体适定性.主要结论是该系统的长时间动力行为.本文证明了系统的拟稳定性,整体吸引子的存在性以及整体吸引子具有有限的分形维数.此外,还证明了指数吸引子的存在性.

Abstract

This paper is concerned with a non-uniform flexible structure with thermal effect governed by Coleman-Gurtin law. By using semi-group method, we establish the global well-posedness of the system. The main result is the long-time dynamics of the system. We prove the quasi-stability property of the system and obtain the existence of a global attractor, and the global attractor has finite fractal dimension. The existence of exponential attractors is also proved.

关键词

柔性结构 / 记忆项 / 拟稳定性 / 整体吸引子 / 指数吸引子

Key words

flexible structure / memory / quasi-stability / global attractor / exponential attractor

引用本文

导出引用
冯保伟, 李海燕. 带有热记忆的非均匀柔性结构的长时间动力行为. 数学学报, 2020, 63(6): 587-600 https://doi.org/10.12386/A2020sxxb0050
Bao Wei FENG, Hai Yan LI. Long-time Dynamics of a Non-uniform Flexible Structure with Thermal Memory. Acta Mathematica Sinica, Chinese Series, 2020, 63(6): 587-600 https://doi.org/10.12386/A2020sxxb0050

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基金

国家自然科学基金(11701465,11701012,61761002);宁夏自然科学基金(2020AAC03233)北方民族大学重大专项(ZDZX201901);北方民族大学校级科研项目(2018XYZSX02)

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