Complete regularity and strong attractor for the strongly damped wave equation with critical nonlinearities on R3
报告人：杨志坚 教授（郑州大学）
报告题目：Complete regularity and strong attractor for the strongly damped wave equation with critical nonlinearities on R3
报告时间：2023.4.24 (周一),8:10-8:50， 地点：励学楼B219
邀请人：李晓军
摘要
In this talk, we investigate the well-posedness and the complete regularity of the weak solutions, and the existence of strong global attractor for the strongly damped wave equation with critical nonlinearities on R3. We show that when both nonlinearities h(x; ut) and g(x; u) are of at most critical growth, (i) the model is well-posed and its weak solution is of higher complete regularity as t > 0, which ensures that the weak solution is exactly the strong one; (ii) the related dynamical system (S(t);H) possesses a strong (H;H2)-global attractor of optimal topological property, which is also the standard global attractor of optimal regularity of S(t) in H. The method developed here allows breaking through the longstanding restriction for this model on R3: the partial regularity of the weak solutions and almost linearity of h(x; ut), and helps obtaining the optimal complete regularity of the weak solutions and the existence of strong global attractor.
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. Diff. Equ.,、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。获得河南省科技进步二等奖1项。