37000gcom威尼斯2023年第13 期数理大讲堂

暨“喜迎90周年校庆”系列讲座第 28期

报告人：杨志坚 郑州大学教授，博士生导师

报告时间：2023年5月24日上午09：30—11：00

地点：数理学院3号楼 3B205

主持人：赵才地 教授

报告题目： Strong attractors for the structurally damped Kirchhoff wave

models with subcritical-critical nonlinearities

报告摘要： In this talk, we are concerned with the well-posedness and the regularity of the solutions, the existence and the continuity of the strong attractors for the structurally damped Kirchhoff wave models with subcritical-critical nonlinearities.We show that when the nonlinearity g(u) is of either critical growth or subcritical growth, while h(ut) is of critical growth, the model is well-posed and its weak solution is exactly the strong one; the related solution semigroup S_(t) has a strong (X; Y )-global attractor and a strong (X; Y )-exponential attractor, which are also the standard global and exponential attractor of optimal regularity of S_(t) in X, respectively, where X is the energy space and Y is the strong solution space; these global attractors are upper semicontinuous and these exponential attractors are H¨older continuous in the sense of Y -topology, respectively. This work is joint with Fang Da and Yue Sun.

报告人简介：

杨志坚  郑州大学理学博士，日本九州大学数理学博士，郑州大学2级教授，博士生导师，河南省跨世纪学术、技术带头人, 河南省高层次人才，美国 《Mathematical Reviews》评论员，《Journal of Partial Differential Equations》期刊编委。主要研究非线性发展方程的整体适定性及无穷维耗散动力系统的长时间动力学行为。主持完成4项国家自然科学基金面上项目；已在《J. Differential Equations》、《Nonlinearity》、《Commun. Contemp. Math.》、《J. Dyn. Differ. Equ.》、《Discrete Contin. Dyn. Syst.》、《J. Evol. Equ.》等国内外SCI期刊上发表研究论文90篇。曾获河南省科技进步二等奖1项。