带有热记忆的非均匀柔性结构的长时间动力行为

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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²1 西南财经大学经济数学学院成都 611130;
2 北方民族大学数学与信息科学学院银川 750021 Long-time Dynamics of a Non-uniform Flexible Structure with Thermal Memory Bao Wei FENG¹, Hai Yan LI²1 Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P. R. China;
2 Mathematics and Information Science, North Minzu University, Yinchuan 750021, P. R. China

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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.

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收稿日期: 2019-08-22

MR (2010):

O175.4

基金资助: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）

通讯作者:李海燕E-mail: lihaiyanmath@163.com

作者简介: 冯保伟,E-mail:bwfeng@swufe.edu.cn

引用本文:

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[J]. 数学学报, 2020, 63(6): 587-600. 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.

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