云亭数学讲坛2022第46讲——李亚男副教授

应学院邀请，哈尔滨工程大学李亚男副教授将作线上学术报告。 

报告题目：Continuity of the attractors in time-dependent spaces and applications

报告摘要：In this talk, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback D-attractor with respect to the perturbations, and an equivalence criterion between their continuity and the pullback equi-attraction, which generalize the continuity theory of attractors developed recently in [Hoang et. al. Proc. Amer. Math. Sc., J. Differential Equations] to that in time-dependent spaces.  (ii) We propose the notion of pullback D-exponential attractor, which includes the notion of time-dependent exponential attractors its special case, and establish its existence and Hölder continuity criterion via quasi-stability method introduced originally by Chueshov andLasiecka. (iii) We apply above-mentioned criteria to the semilinear damped wave equations with perturbed time-dependent speed of propagation to realize above mentioned continuity of pullback D and D-exponential attractors in time-dependent phase spaces, and the method developed here allows to overcome the difficulty of the hyperbolicity of the model.

报告时间：2022年7月8日下午4:30

报告地点：腾讯会议号234170179

邀 请 人：马巧珍 教授

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报告人简介

      李亚男，哈尔滨工程大学数学科学学院副教授，硕士生导师，2020年于郑州大学取得博士学位，导师杨志坚教授。主要从事Kirchhoff波动方程等不同类型的非线性耗散波动方程解的长时间动力学行为的研究。主持国家自然科学基金青年项目一项，黑龙江省自然科学基金联合引导项目一项，在JDE，DCDS，JDDE，AMO等杂志发表学术论文10余篇。